Professor Nalini Joshi

FAA

F07 - Carslaw Building
The University of Sydney

Telephone 9351 2172
Fax 9351 4534

Website Personal web page

Biographical details

Payne-Scott Professor Nalini Joshi AO is Chair of Applied Mathematics at the University of Sydney, and a Georgina Sweet Australian Laureate Fellow.

Nalini was born and spent her early childhood in Burma, before her family emigrated to Australia. She was awarded a BSc (Hons), with the University Medal in applied mathematics, by the University of Sydney and then a PhD in computational and applied mathematics by Princeton University in the USA.

Her research focuses on mathematical methods to study integrable systems, which arise as universal models everywhere. Nalini's strong research achievements led to several distinctions. She was elected as a Fellow of the Australian Academy of Science in 2008, won an Australian Research Council Georgina Sweet Australian Laureate Fellowship in 2012 and was the 150th AnniversaryHardy Fellow of the London Mathematical Society in 2015.

Nalini also has a keen intereset in diversity and her Laureate Fellowship had a component to attract and retain female researchers in STEM. She was foundation co-Chair of the SAGE (Science in Australia Gender Equity) national initiative, which is currently running a pilot program that involves 44 research organisations in Australia, including 33 universities.

In the 2016 Queen’s Birthday honours, Nalini was appointed an Officer of the Order of Australia for distinguished service to mathematical science and tertiary education as an academic, author and researcher, to professional societies, and as a role model and mentor of young mathematicians.

Research interests

Nalini's research focuses on ways to describe special functions that are universal in applications. In a way they have properties like the transcendental number π, which cannot be expressed as a finite combination of simpler numbers. Yet, they appear in applications everywhere. For example, they describe

interaction of heavy atomic particles
quantum gravity
distribution of bus arrival times in Cuernavaca, the New York subway system and flight boarding times
  • the distribution of large prime numbers;
  • electric fields in electrolyte solutions;
  • magnetic fields and waves in plasma physics;
  • water waves in the oceans;
  • stationary solutions of Einstein’s equations of general relativity;
  • cloud formations in the atmosphere;
  • aircraft boarding times;
  • bus arrival times;
  • the New York subway system;

and many, many other applications.

Nalini describes her research as solving mathematical puzzles that allow her to know these functions better.

These puzzles involve non-linear differential and difference equations, which are studied through various techniques, including algebraic geometry, topology, and asymptotic methods in limits. The differential and difference equations she studies are called integrable systems. When they involve one independent variable, they are usually the Painlevé equations, while in two or more dimensions, the equations are soliton equations.

The mathematical tools used are at a high level. For example, instead of describing solutions analytically by changing an independent variable like time, they can be tracked by initial values that the solutions move through. It's like following circular arcs of light in the sky at night that are created by stars. In the same way, the solutions of dynamical systems follow certain trajectories starting at some point in the space of all initial values. It turns out that the geometry of this space gives us a great deal of information about the global nature of all possible solutions.

It turns out that this also leads to some deep algebraic descriptions of the solutions, given by reflection groups. The discrete Painlevé equations turn out to be given by translations (or walks) on lattices created by affine reflection groups. The results are very pretty and beautiful.

Her research papers and books can be found on her publication page or her OrCiD page.

Specific research areas: Integrable systems, the Painlevé equations, discrete Painlevé equations, lattice equations, geometric asymptotics, nonlinear dynamics, nonlinear waves, perturbation theory.

Teaching and supervision

See Nalini's course on integrable systems. Nalini is currently supervising several PhD projects in this area, which propose to extend the mathematical toolbox to describe solutions of non-linear differential and discrete equations.

Timetable

N_Joshi

Awards and honours

Fellow of the Australian Academy of Science (elected 2008)

ARC Georgina Sweet Australian Laureate Fellowship (2012-18)

AFR Westpac 100 Women of Influence (2016)

Payne-Scott Professorial Distinction (2016)

Eureka award for Outstanding Mentor of Young Researchers (2018)

International links

United Kingdom

(The University of Leeds) I collaborate with Professor Frank W. Nijhoff, who is the Professor of Mathematical Physics. Currently, I am co-writing a book with him and Professor Jarmo Hietarinta from the University of Turku in Finland.

United Kingdom

(The University of Leeds) Visiting Professor

Selected grants

2016

  • Reflection Groups and Discrete Dynamical Systems; Joshi N, Kajiwara K; Australian Research Council (ARC)/Discovery Projects (DP).

2013

  • Critical solutions of nonlinear systems; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2012

  • Geometric construction of critical solutions of nonlinear systems; Joshi N; Australian Research Council (ARC)/Australian Laureate Fellowships (FL).

2011

  • Geometry and Analysis of Discrete Integrable Systems; Dullin H, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2010

  • Random and integrable models in mathematical physics (RIMMP); Grava T, Klein C, Joshi N; European Commission (Belgium)/Marie Curie Action: International Research Staff Exchange (IRSES).

2009

  • A national discipline-specific professional development programme for lecturers and tutors in the ma; Bower M, Vu T, Bloom W, Donovan D, Brown N, Skalicky J, L'och B, Joshi N, Wood L; Australian Learning and Teaching Council/Leadership for Excellence.
  • Integrable Lattice Equations; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2008

  • Integrable Lattice Equations; Joshi N; University of Sydney/Bridging Support.

2006

  • New Directions in Non-linear Mathematical Asymptotics; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2005

  • Integrable functional and delay differential equations; Cosgrove C, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).

2003

  • Global Behaviour of Integrable Complex Systems; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
  • Mathematical biosciences network; Joshi N; Australian Research Council (ARC)/Special Research Initiatives.

2002

  • Singularities And Classifications Of Integrable Systems; Joshi N, Cosgrove C; Australian Research Council (ARC)/Discovery Projects (DP).

1997

  • Asymptotics and integrability of nonlinear differential and difference equations; Joshi N; Australian Research Council (ARC)/Australian Senior Research Fellowship.

Selected publications

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Books

  • Hietarinta, J., Joshi, N., Nijhoff, F. (2016). Discrete Systems and Integrability. Cambridge: Cambridge University Press. [More Information]

Book Chapters

  • Kruskal, M., Joshi, N., Halburd, R. (2004). Analytical And Asymptotic Methods For Nonlinear Singularity Analysis: A Review And Extensions Of Tests For The Painlevé Property. In Basil Grammaticos, Yvette Kosmann-Schwarzbach, K. M. Tamizhmani (Eds.), Integrability of Nonlinear Systems, (pp. 175-208). Berlin: Springer.
  • Joshi, N. (2003). Hunting mathematical butterflies. In Ball, Akhmediev (Eds.), Nonlinear Dynamics: from Lasers to Butterflies, (pp. 77-114). USA: World Scientific Publishing.

Journals

  • Joshi, N., Lustri, C. (2019). Generalized solitary waves in a finite-difference Korteweg-de Vries equation. Studies in Applied Mathematics, 142, 359-384q. [More Information]
  • Joshi, N., Pelinovsky, D. (2019). Integrable semi-discretization of the massive Thirring system in laboratory coordinates. Journal of Physics A: Mathematical and Theoretical, 52(3), Art. 03LT01 - 1-Art. 03LT01 - 12. [More Information]
  • Joshi, N., Lustri, C., Luu, S. (2019). Nonlinear q-Stokes phenomena for q-Painlev� I. Journal of Physics A: Mathematical and Theoretical, 52(6), Art. 065204-30 pages. [More Information]
  • Joshi, N., Radnovic, M. (2018). Asymptotic behaviour of the fifth Painleve transcendents in the space of initial values. Proceedings of the London Mathematical Society, 3(116), 1329-1364. [More Information]
  • Joshi, N., Liu, Q. (2018). Asymptotic behaviours given by elliptic functions in PI-PV. Nonlinearity, 31(8), 3726-3747. [More Information]
  • Joshi, N., Nakazono, N. (2017). Elliptic Painleve equations from next-nearest-neighbor translations on the E8(1) lattice. Journal of Physics A: Mathematical and Theoretical, 50, 1-17. [More Information]
  • Joshi, N., Kajiwara, K., Masuda, T., Nakazono, N., Shi, Y. (2017). Geometric description of a discrete power function associated with the sixth Painlev� equation. Proceedings of the Royal Society A, A473 (Art. 20170312), 1-19. [More Information]
  • Joshi, N., Takei, Y. (2017). On stokes phenomena for the alternate discrete PI equation. Trends in Mathematics, Part F2, 369-381. [More Information]
  • Joshi, N., Lustri, C., Luu, S. (2017). Stokes phenomena in discrete Painleve II. Proceedings of the Royal Society A, 473(2198), 1-20. [More Information]
  • Joshi, N., Takei, Y. (2017). Toward the exact WKB analysis of discrete Painleve equations. Publications of the Research Institute for Mathematical Sciences, B61(2017), 83-96.
  • Joshi, N., Roffelsen, P. (2016). Analytic solutions of q-P(A1) near its critical points. Nonlinearity, 29(12), 3696-3742. [More Information]
  • Joshi, N., Radnovic, M. (2016). Asymptotic Behavior of the Fourth Painleve Transcendents in the Space of Initial Values. Constructive Approximation, 44(2), 195-231. [More Information]
  • Atkinson, J., Howes, P., Joshi, N., Nakazono, N. (2016). Geometry of an elliptic difference equation related to Q4. Journal of The London Mathematical Society, 93(3), 763-784. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2016). Lattice equations arising from discrete Painleve systems: II. A4(1)case. Journal of Physics A: Mathematical and Theoretical, 49, 1-39. [More Information]
  • Joshi, N., Nakazono, N. (2016). Lax pairs of discrete Painleve equations: (A2 + A1)(1) case. Proceedings of the Royal Society A, 472(2196), 1-14. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2016). Reflection groups and discrete integrable systems. Journal of Integrable Systems, 1(1), 1-37. [More Information]
  • Joshi, N., Lobb, S. (2016). Singular dynamics of a q-difference Painleve equation in its initial-value space. Journal of Physics A: Mathematical and Theoretical, 49(1), 1-24. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2015). Lattice equations arising from discrete Painlev systems. I. (A 2 + A 1)(1) and ( A 1 + A 1 ) ( 1 ) cases. Journal of Mathematical Physics, 56(9), 092705-1-092705-25. [More Information]
  • Joshi, N. (2015). Quicksilver Solutions of a q-Difference First Painleve Equation. Studies in Applied Mathematics, 134(2), 233-251. [More Information]
  • Joshi, N., Lustri, C. (2015). Stokes phenomena in discrete Painlevé I. Proceedings of the Royal Society A, 471(2177), 1-22. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2014). Geometric reductions of ABS equations on an n-cube to discrete Painlevé systems. Journal of Physics A: Mathematical and Theoretical, 47(50), 1-16. [More Information]
  • Howes, P., Joshi, N. (2014). Global Asymptotics of the Second Painlev Equation in Okamoto's Space. Constructive Approximation, 39(1), 11-41. [More Information]
  • Atkinson, J., Joshi, N. (2013). Singular-Boundary Reductions of Type-Q ABS Equations. International Mathematics Research Notices, 7, 1451-1481. [More Information]
  • Joshi, N., Shi, Y. (2012). Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions. Proceedings of the Royal Society A, 468(2146), 3247-3264. [More Information]
  • Atkinson, J., Joshi, N. (2012). The Schwarzian variable associated with discrete KdV-type equations. Nonlinearity, 25(6), 1851-1866. [More Information]
  • Joshi, N., Shi, Y. (2011). Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions. Proceedings of the Royal Society A, 467, 3443-3468. [More Information]
  • Duistermaat, J., Joshi, N. (2011). Okamoto's Space for the First Painlevé Equation in Boutroux Coordinates. Archive for Rational Mechanics and Analysis, 202(3), 707-785. [More Information]
  • Wood, L., Vu, T., Bower, M., Brown, N., Skalicky, J., Donovan, D., L'och, B., Joshi, N., Bloom, W. (2011). Professional development for teaching in higher education. International Journal of Mathematical Education in Science and Technology, 42(7), 997-1009. [More Information]
  • Butler, S., Joshi, N. (2010). An inverse scattering transform for the lattice potential KdV equation. Inverse Problems, 26(115012), 1-28. [More Information]
  • Kassotakis, P., Joshi, N. (2010). Integrable Non-QRT Mappings of the Plane. Letters in Mathematical Physics, 91(1), 71-81. [More Information]
  • Ramani, A., Grammaticos, B., Joshi, N. (2010). Second-degree discrete Painlevé equations conceal first-degree ones. Journal of Physics A: Mathematical and Theoretical, 43(17), 1-9. [More Information]
  • Joshi, N., Spicer, P. (2009). Direct "Delay" Reductions of the Toda Hierarchy. Journal of the Physical Society of Japan, 78(9), 094006-1-094006-5. [More Information]
  • Joshi, N. (2009). Direct 'delay' reductions of the Toda equation. Journal of Physics A: Mathematical and Theoretical, 42(2), 1-8. [More Information]
  • Joshi, N., Morrison, T. (2009). Existence and uniqueness of Tronquee solutions of the fourth-order Jimbo-Miwa second Painleve equation. Proceedings of the American Mathematical Society, 137(6), 2005-2014. [More Information]
  • Joshi, N., Lafortune, S., Ramani, A. (2009). Hirota bilinear formalism and ultra-discrete singularity analysis. Nonlinearity, 22(4), 871-887. [More Information]
  • Joshi, N., Kitaev, A., Treharne, P. (2009). On the linearization of the first and second Painleve equations. Journal of Physics A: Mathematical and Theoretical, 42(5), 055208-1-055208-18. [More Information]
  • Joshi, N., Morrison, T. (2008). New exact solutions of spatially and temporally varying reaction-diffusion equations. Analysis and Applications, 6(4), 371-381. [More Information]
  • Field, C., Joshi, N., Nijhoff, F. (2008). q-difference equations of kd V type and Chazy-type second degree difference equations. Journal of Physics A: Mathematical and Theoretical, 41, 332005-332018. [More Information]
  • Hay, M., Hietarinta, J., Joshi, N., Nijhoff, F. (2007). A Lax pair for a lattice modified KdV equation, reductions to q-Painleve equations and associated Lax pairs. Journal of Physics A: Mathematical and Theoretical, 40(2), F61-F73. [More Information]
  • Joshi, N., Kitaev, A., Treharne, P. (2007). On the linearization of the Painleve' III-VI equations and reductions of the three-wave resonant system. Journal of Mathematical Physics, 48(10), 103512-1-103512-42. [More Information]
  • Joshi, N., Ormerod, C. (2007). The general theory of linear difference equations over the max-plus semi-ring. Studies in Applied Mathematics, 118(1), 85-97. [More Information]
  • Clarkson, P., Joshi, N., Mazzocco, M. (2007). The Lax Pair for the mKdV Hierarchy. Seminaires et Congres, 14(Theories Asymptotiques et Equations de Painleve), 53-64.
  • Ramani, A., Joshi, N., Grammaticos, B., Tamizhmani, T. (2006). Deconstructing an integrable lattice equation. Journal of Physics A: Mathematical and General, 39(8), L145-L149. [More Information]
  • Joshi, N., Grammaticos, B., Tamizhmani, T., Ramani, A. (2006). From integrable lattices to non-QRT mappings. Letters in Mathematical Physics, 78(1), 27-37. [More Information]
  • Joshi, N., Pickering, A. (2006). Generalized Halphen systems. Proceedings of the Royal Society of Edinburgh Section A (Mathematics), 136A (6), 1287-1301. [More Information]
  • Joshi, N., Kajiwara, K., Mazzocco, M. (2006). Generating function associated with the Hankel determinant formula for the solutions of the Painlevé IV equation. Funkcialaj Ekvacioj, Serio Internacia, 49(3), 451-468.
  • Joshi, N., Lafortune, S. (2006). Integrable ultra-discrete equations and singularity analysis. Nonlinearity, 19(6), 1295-1312. [More Information]
  • Gordoa, P., Joshi, N., Pickering, A. (2006). Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems. Journal of Mathematical Physics, 47(7), 073504-1-073504-16. [More Information]
  • Gordoa, P., Joshi, N., Pickering, A. (2005). Backlund transformations for fourth Painleve hierarchies. Journal of Differential Equations, 217(1), 124-153. [More Information]
  • Joshi, N., Lafortune, S. (2005). How to detect integrability in cellular automata. Journal of Physics A: Mathematical and General, 38(28), L499-L504. [More Information]
  • Joshi, N., Kitaev, A. (2005). The Dirichlet boundary value problem for real solutions of the first Painleve equation on segments in non-positive semi-axis. Journal fur die Reine und Angewandte Mathematik (Crelle's journal), 583, 29-86. [More Information]
  • Joshi, N., Kajiwara, K., Mazzocco, M. (2004). Generating Function Associated With The Determinant Formula For The Solutions Of The Painlevé II Equation. Asterisque, 297(2004), 67-78.
  • Joshi, N., Nijhoff, F., Ormerod, C. (2004). Lax pairs for ultra-discrete Painlevé cellular automata. Journal of Physics A: Mathematical and General, 37(2004), L559-L565. [More Information]
  • Joshi, N. (2004). The second Painleve hierarchy and the stationary KdV hierarchy. Publications of the Research Institute for Mathematical Sciences, 40(2004), 1039-1061. [More Information]
  • Gordoa, P., Joshi, N., Pickering, A. (2003). A new technique in nonlinear singularity analysis. Publications of the Research Institute for Mathematical Sciences, 39, 435-449. [More Information]
  • Maruno, K., Ohta, Y., Joshi, N. (2003). Exact localized solutions of quintic discrete nonlinear Schrodinger equation. Physics Letters. Section A: General, Atomic and Solid State Physics, 311(2-3), 214-220. [More Information]
  • Joshi, N., Mazzocco, M. (2003). Existence and uniqueness of tri-tronquee solutions of the second Painlevé hierarchy. Nonlinearity, 16(2), 427-439. [More Information]
  • Clarkson, P., HONE, A., Joshi, N. (2003). Hierarchies of difference equations and Backlund transformations. Journal Of Nonlinear Mathematical Physics, 10(Suppl 2), 13-26.
  • Joshi, N. (2003). Tritronquee solutions of perturbed first painleve equations. Theoretical and Mathematical Physics, 11, 1515-1519. [More Information]
  • HONE, A., Joshi, N., Kitaev, A. (2002). An entire function defined by a nonlinear recurrence relation. Journal of The London Mathematical Society, 66(2), 377-387. [More Information]
  • CRESSWELL, C., Joshi, N. (2002). Consistent composition of Backlund transformations produces confined maps. Letters in Mathematical Physics, 61(1), 1-14. [More Information]
  • Gordoa, P., Joshi, N., Pickering, I. (2001). Mappings preserving locations of movable poles: II. The third and fifth Painlevé equations. Nonlinearity, 14(3), 567-582.
  • Gordoa, P., Joshi, N., Pickering, I. (2001). On a Generalized 2 + 1 Dspersive Water Wave Hierarchy. Publications of the Research Institute for Mathematical Sciences, 37, 327-347.
  • Joshi, N., Kitaev, A. (2001). On Boutroux's Tritronquée Solutions of the First Painlevé Equation. Studies in Applied Mathematics, 107(3), 253-291.
  • Joshi, N. (2001). Regularizing the KdV equation near a blow-up surface. Theoretical and Mathematical Physics, 127(3), 744-750.
  • Gordoa, P., Joshi, N., Pickering, I. (2001). Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations. Glasgow Mathematical Journal, 43(A), 23-32.
  • Cresswell, C., Joshi, N. (1999). The discrete first, second and thirty-fourth Painleve hierarchies. Journal of Physics A: Mathematical and General, 32(4), 655-669.

Edited Journals

  • Joshi, N., Noumi, M., Sakai, H., Viallet, C. (2013). Journal of Nonlinear Mathematical Physics. Journal Of Nonlinear Mathematical Physics, 20(Supplement 1).

Conferences

  • Joshi, N., Atkinson, J., Howes, P., Nakazono, N. (2012). Extension of a one-dimensional reduction of the Q4 mapping to a discrete Painleve equation. The Japan Society for Industrial and Applied Mathematics 2012.
  • Brown, N., Bower, M., Skalicky, J., Wood, L., Donovan, D., L'och, B., Bloom, W., Joshi, N. (2010). A professional development framework for teaching in higher education. 33rd Higher Education Research and Development Society of Australasia International Conference: HERDSA 2010 Reshaping Higher Education, Milperra: Higher Education Research and Development Society of Australasia.
  • Joshi, N. (2005). Asymptotics for Extended Cellular Automata. Recent Trends in Exponential Asymptotics, Kyoto: RIMS.
  • Cresswell, C., Joshi, N. (1999). The discrete Painleve I hierarchy. Symmetries and Integrability of Difference Equations, UK: Cambridge University Press. [More Information]

2019

  • Joshi, N., Lustri, C. (2019). Generalized solitary waves in a finite-difference Korteweg-de Vries equation. Studies in Applied Mathematics, 142, 359-384q. [More Information]
  • Joshi, N., Pelinovsky, D. (2019). Integrable semi-discretization of the massive Thirring system in laboratory coordinates. Journal of Physics A: Mathematical and Theoretical, 52(3), Art. 03LT01 - 1-Art. 03LT01 - 12. [More Information]
  • Joshi, N., Lustri, C., Luu, S. (2019). Nonlinear q-Stokes phenomena for q-Painlev� I. Journal of Physics A: Mathematical and Theoretical, 52(6), Art. 065204-30 pages. [More Information]

2018

  • Joshi, N., Radnovic, M. (2018). Asymptotic behaviour of the fifth Painleve transcendents in the space of initial values. Proceedings of the London Mathematical Society, 3(116), 1329-1364. [More Information]
  • Joshi, N., Liu, Q. (2018). Asymptotic behaviours given by elliptic functions in PI-PV. Nonlinearity, 31(8), 3726-3747. [More Information]

2017

  • Joshi, N., Nakazono, N. (2017). Elliptic Painleve equations from next-nearest-neighbor translations on the E8(1) lattice. Journal of Physics A: Mathematical and Theoretical, 50, 1-17. [More Information]
  • Joshi, N., Kajiwara, K., Masuda, T., Nakazono, N., Shi, Y. (2017). Geometric description of a discrete power function associated with the sixth Painlev� equation. Proceedings of the Royal Society A, A473 (Art. 20170312), 1-19. [More Information]
  • Joshi, N., Takei, Y. (2017). On stokes phenomena for the alternate discrete PI equation. Trends in Mathematics, Part F2, 369-381. [More Information]
  • Joshi, N., Lustri, C., Luu, S. (2017). Stokes phenomena in discrete Painleve II. Proceedings of the Royal Society A, 473(2198), 1-20. [More Information]
  • Joshi, N., Takei, Y. (2017). Toward the exact WKB analysis of discrete Painleve equations. Publications of the Research Institute for Mathematical Sciences, B61(2017), 83-96.

2016

  • Joshi, N., Roffelsen, P. (2016). Analytic solutions of q-P(A1) near its critical points. Nonlinearity, 29(12), 3696-3742. [More Information]
  • Joshi, N., Radnovic, M. (2016). Asymptotic Behavior of the Fourth Painleve Transcendents in the Space of Initial Values. Constructive Approximation, 44(2), 195-231. [More Information]
  • Hietarinta, J., Joshi, N., Nijhoff, F. (2016). Discrete Systems and Integrability. Cambridge: Cambridge University Press. [More Information]
  • Atkinson, J., Howes, P., Joshi, N., Nakazono, N. (2016). Geometry of an elliptic difference equation related to Q4. Journal of The London Mathematical Society, 93(3), 763-784. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2016). Lattice equations arising from discrete Painleve systems: II. A4(1)case. Journal of Physics A: Mathematical and Theoretical, 49, 1-39. [More Information]
  • Joshi, N., Nakazono, N. (2016). Lax pairs of discrete Painleve equations: (A2 + A1)(1) case. Proceedings of the Royal Society A, 472(2196), 1-14. [More Information]
  • Joshi, N., Nakazono, N., Shi, Y. (2016). Reflection groups and discrete integrable systems. Journal of Integrable Systems, 1(1), 1-37. [More Information]
  • Joshi, N., Lobb, S. (2016). Singular dynamics of a q-difference Painleve equation in its initial-value space. Journal of Physics A: Mathematical and Theoretical, 49(1), 1-24. [More Information]

2015

  • Joshi, N., Nakazono, N., Shi, Y. (2015). Lattice equations arising from discrete Painlev systems. I. (A 2 + A 1)(1) and ( A 1 + A 1 ) ( 1 ) cases. Journal of Mathematical Physics, 56(9), 092705-1-092705-25. [More Information]
  • Joshi, N. (2015). Quicksilver Solutions of a q-Difference First Painleve Equation. Studies in Applied Mathematics, 134(2), 233-251. [More Information]
  • Joshi, N., Lustri, C. (2015). Stokes phenomena in discrete Painlevé I. Proceedings of the Royal Society A, 471(2177), 1-22. [More Information]

2014

  • Joshi, N., Nakazono, N., Shi, Y. (2014). Geometric reductions of ABS equations on an n-cube to discrete Painlevé systems. Journal of Physics A: Mathematical and Theoretical, 47(50), 1-16. [More Information]
  • Howes, P., Joshi, N. (2014). Global Asymptotics of the Second Painlev Equation in Okamoto's Space. Constructive Approximation, 39(1), 11-41. [More Information]

2013

  • Joshi, N., Noumi, M., Sakai, H., Viallet, C. (2013). Journal of Nonlinear Mathematical Physics. Journal Of Nonlinear Mathematical Physics, 20(Supplement 1).
  • Atkinson, J., Joshi, N. (2013). Singular-Boundary Reductions of Type-Q ABS Equations. International Mathematics Research Notices, 7, 1451-1481. [More Information]

2012

  • Joshi, N., Shi, Y. (2012). Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions. Proceedings of the Royal Society A, 468(2146), 3247-3264. [More Information]
  • Joshi, N., Atkinson, J., Howes, P., Nakazono, N. (2012). Extension of a one-dimensional reduction of the Q4 mapping to a discrete Painleve equation. The Japan Society for Industrial and Applied Mathematics 2012.
  • Atkinson, J., Joshi, N. (2012). The Schwarzian variable associated with discrete KdV-type equations. Nonlinearity, 25(6), 1851-1866. [More Information]

2011

  • Joshi, N., Shi, Y. (2011). Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions. Proceedings of the Royal Society A, 467, 3443-3468. [More Information]
  • Duistermaat, J., Joshi, N. (2011). Okamoto's Space for the First Painlevé Equation in Boutroux Coordinates. Archive for Rational Mechanics and Analysis, 202(3), 707-785. [More Information]
  • Wood, L., Vu, T., Bower, M., Brown, N., Skalicky, J., Donovan, D., L'och, B., Joshi, N., Bloom, W. (2011). Professional development for teaching in higher education. International Journal of Mathematical Education in Science and Technology, 42(7), 997-1009. [More Information]

2010

  • Brown, N., Bower, M., Skalicky, J., Wood, L., Donovan, D., L'och, B., Bloom, W., Joshi, N. (2010). A professional development framework for teaching in higher education. 33rd Higher Education Research and Development Society of Australasia International Conference: HERDSA 2010 Reshaping Higher Education, Milperra: Higher Education Research and Development Society of Australasia.
  • Butler, S., Joshi, N. (2010). An inverse scattering transform for the lattice potential KdV equation. Inverse Problems, 26(115012), 1-28. [More Information]
  • Kassotakis, P., Joshi, N. (2010). Integrable Non-QRT Mappings of the Plane. Letters in Mathematical Physics, 91(1), 71-81. [More Information]
  • Ramani, A., Grammaticos, B., Joshi, N. (2010). Second-degree discrete Painlevé equations conceal first-degree ones. Journal of Physics A: Mathematical and Theoretical, 43(17), 1-9. [More Information]

2009

  • Joshi, N., Spicer, P. (2009). Direct "Delay" Reductions of the Toda Hierarchy. Journal of the Physical Society of Japan, 78(9), 094006-1-094006-5. [More Information]
  • Joshi, N. (2009). Direct 'delay' reductions of the Toda equation. Journal of Physics A: Mathematical and Theoretical, 42(2), 1-8. [More Information]
  • Joshi, N., Morrison, T. (2009). Existence and uniqueness of Tronquee solutions of the fourth-order Jimbo-Miwa second Painleve equation. Proceedings of the American Mathematical Society, 137(6), 2005-2014. [More Information]
  • Joshi, N., Lafortune, S., Ramani, A. (2009). Hirota bilinear formalism and ultra-discrete singularity analysis. Nonlinearity, 22(4), 871-887. [More Information]
  • Joshi, N., Kitaev, A., Treharne, P. (2009). On the linearization of the first and second Painleve equations. Journal of Physics A: Mathematical and Theoretical, 42(5), 055208-1-055208-18. [More Information]

2008

  • Joshi, N., Morrison, T. (2008). New exact solutions of spatially and temporally varying reaction-diffusion equations. Analysis and Applications, 6(4), 371-381. [More Information]
  • Field, C., Joshi, N., Nijhoff, F. (2008). q-difference equations of kd V type and Chazy-type second degree difference equations. Journal of Physics A: Mathematical and Theoretical, 41, 332005-332018. [More Information]

2007

  • Hay, M., Hietarinta, J., Joshi, N., Nijhoff, F. (2007). A Lax pair for a lattice modified KdV equation, reductions to q-Painleve equations and associated Lax pairs. Journal of Physics A: Mathematical and Theoretical, 40(2), F61-F73. [More Information]
  • Joshi, N., Kitaev, A., Treharne, P. (2007). On the linearization of the Painleve' III-VI equations and reductions of the three-wave resonant system. Journal of Mathematical Physics, 48(10), 103512-1-103512-42. [More Information]
  • Joshi, N., Ormerod, C. (2007). The general theory of linear difference equations over the max-plus semi-ring. Studies in Applied Mathematics, 118(1), 85-97. [More Information]
  • Clarkson, P., Joshi, N., Mazzocco, M. (2007). The Lax Pair for the mKdV Hierarchy. Seminaires et Congres, 14(Theories Asymptotiques et Equations de Painleve), 53-64.

2006

  • Ramani, A., Joshi, N., Grammaticos, B., Tamizhmani, T. (2006). Deconstructing an integrable lattice equation. Journal of Physics A: Mathematical and General, 39(8), L145-L149. [More Information]
  • Joshi, N., Grammaticos, B., Tamizhmani, T., Ramani, A. (2006). From integrable lattices to non-QRT mappings. Letters in Mathematical Physics, 78(1), 27-37. [More Information]
  • Joshi, N., Pickering, A. (2006). Generalized Halphen systems. Proceedings of the Royal Society of Edinburgh Section A (Mathematics), 136A (6), 1287-1301. [More Information]
  • Joshi, N., Kajiwara, K., Mazzocco, M. (2006). Generating function associated with the Hankel determinant formula for the solutions of the Painlevé IV equation. Funkcialaj Ekvacioj, Serio Internacia, 49(3), 451-468.
  • Joshi, N., Lafortune, S. (2006). Integrable ultra-discrete equations and singularity analysis. Nonlinearity, 19(6), 1295-1312. [More Information]
  • Gordoa, P., Joshi, N., Pickering, A. (2006). Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems. Journal of Mathematical Physics, 47(7), 073504-1-073504-16. [More Information]

2005

  • Joshi, N. (2005). Asymptotics for Extended Cellular Automata. Recent Trends in Exponential Asymptotics, Kyoto: RIMS.
  • Gordoa, P., Joshi, N., Pickering, A. (2005). Backlund transformations for fourth Painleve hierarchies. Journal of Differential Equations, 217(1), 124-153. [More Information]
  • Joshi, N., Lafortune, S. (2005). How to detect integrability in cellular automata. Journal of Physics A: Mathematical and General, 38(28), L499-L504. [More Information]
  • Joshi, N., Kitaev, A. (2005). The Dirichlet boundary value problem for real solutions of the first Painleve equation on segments in non-positive semi-axis. Journal fur die Reine und Angewandte Mathematik (Crelle's journal), 583, 29-86. [More Information]

2004

  • Kruskal, M., Joshi, N., Halburd, R. (2004). Analytical And Asymptotic Methods For Nonlinear Singularity Analysis: A Review And Extensions Of Tests For The Painlevé Property. In Basil Grammaticos, Yvette Kosmann-Schwarzbach, K. M. Tamizhmani (Eds.), Integrability of Nonlinear Systems, (pp. 175-208). Berlin: Springer.
  • Joshi, N., Kajiwara, K., Mazzocco, M. (2004). Generating Function Associated With The Determinant Formula For The Solutions Of The Painlevé II Equation. Asterisque, 297(2004), 67-78.
  • Joshi, N., Nijhoff, F., Ormerod, C. (2004). Lax pairs for ultra-discrete Painlevé cellular automata. Journal of Physics A: Mathematical and General, 37(2004), L559-L565. [More Information]
  • Joshi, N. (2004). The second Painleve hierarchy and the stationary KdV hierarchy. Publications of the Research Institute for Mathematical Sciences, 40(2004), 1039-1061. [More Information]

2003

  • Gordoa, P., Joshi, N., Pickering, A. (2003). A new technique in nonlinear singularity analysis. Publications of the Research Institute for Mathematical Sciences, 39, 435-449. [More Information]
  • Maruno, K., Ohta, Y., Joshi, N. (2003). Exact localized solutions of quintic discrete nonlinear Schrodinger equation. Physics Letters. Section A: General, Atomic and Solid State Physics, 311(2-3), 214-220. [More Information]
  • Joshi, N., Mazzocco, M. (2003). Existence and uniqueness of tri-tronquee solutions of the second Painlevé hierarchy. Nonlinearity, 16(2), 427-439. [More Information]
  • Clarkson, P., HONE, A., Joshi, N. (2003). Hierarchies of difference equations and Backlund transformations. Journal Of Nonlinear Mathematical Physics, 10(Suppl 2), 13-26.
  • Joshi, N. (2003). Hunting mathematical butterflies. In Ball, Akhmediev (Eds.), Nonlinear Dynamics: from Lasers to Butterflies, (pp. 77-114). USA: World Scientific Publishing.
  • Joshi, N. (2003). Tritronquee solutions of perturbed first painleve equations. Theoretical and Mathematical Physics, 11, 1515-1519. [More Information]

2002

  • HONE, A., Joshi, N., Kitaev, A. (2002). An entire function defined by a nonlinear recurrence relation. Journal of The London Mathematical Society, 66(2), 377-387. [More Information]
  • CRESSWELL, C., Joshi, N. (2002). Consistent composition of Backlund transformations produces confined maps. Letters in Mathematical Physics, 61(1), 1-14. [More Information]

2001

  • Gordoa, P., Joshi, N., Pickering, I. (2001). Mappings preserving locations of movable poles: II. The third and fifth Painlevé equations. Nonlinearity, 14(3), 567-582.
  • Gordoa, P., Joshi, N., Pickering, I. (2001). On a Generalized 2 + 1 Dspersive Water Wave Hierarchy. Publications of the Research Institute for Mathematical Sciences, 37, 327-347.
  • Joshi, N., Kitaev, A. (2001). On Boutroux's Tritronquée Solutions of the First Painlevé Equation. Studies in Applied Mathematics, 107(3), 253-291.
  • Joshi, N. (2001). Regularizing the KdV equation near a blow-up surface. Theoretical and Mathematical Physics, 127(3), 744-750.
  • Gordoa, P., Joshi, N., Pickering, I. (2001). Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations. Glasgow Mathematical Journal, 43(A), 23-32.

1999

  • Cresswell, C., Joshi, N. (1999). The discrete first, second and thirty-fourth Painleve hierarchies. Journal of Physics A: Mathematical and General, 32(4), 655-669.
  • Cresswell, C., Joshi, N. (1999). The discrete Painleve I hierarchy. Symmetries and Integrability of Difference Equations, UK: Cambridge University Press. [More Information]

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