Dr James Atkinson

F07 - Carslaw Building
The University of Sydney

Telephone 9351 2971
Fax 9351 4534

Website Personal web page

Biographical details

Academic history

2011-2013 Australian post-doctoral fellow, School of Mathematics and Statistics, University of Sydney, Australia

2009-2010 Postdoc, School of Mathematics and Statistics, University of Sydney, Australia 2008-2009 Research associate, Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia

2004-2008 PhD (Integrable lattice equations: Connection to the Mobius group, Backlund transformations and solutions), Department of Applied Mathematics, University of Leeds, UK

2003-2004 MSc (The Numerical Solution of Differential Equations), University of Reading, UK

1997-2001 BSc (Physics with Acoustics), University of Surrey, Guildford, UK

Research interests

I am involved in tackling questions about discrete integrable systems. In particular quadrilateral lattice equations which are fully discrete counterparts of integrable partial differential equations of Korteweg-de Vries type. I am supported by the Austrailian Research Council (Grant number DP 110104151).

Teaching and supervision

Timetable

Selected grants

2011

  • Algebraic interpretations of discrete integrable equations; Atkinson J; Australian Research Council (ARC)/Discovery Projects (DP).

Selected publications

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Journals

  • Atkinson, J., Joshi, N. (2013). Singular-Boundary Reductions of Type-Q ABS Equations. International Mathematics Research Notices, 7, 1451-1481. [More Information]
  • Atkinson, J. (2012). A multidimensionally consistent version of Hirota's discrete KdV equation. Journal of Physics A: Mathematical and Theoretical, 45(22), 222001-1-222001-10. [More Information]
  • Atkinson, J., Lobb, S., Nijhoff, F. (2012). An integrable multicomponent quad-equation and its Lagrangian formulation. Theoretical and Mathematical Physics, 173(3), 1644-1653. [More Information]
  • Atkinson, J., Joshi, N. (2012). The Schwarzian variable associated with discrete KdV-type equations. Nonlinearity, 25(6), 1851-1866. [More Information]
  • Atkinson, J. (2011). Singularities of Type-Q ABS Equations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7(article 073), 073-1-073-14. [More Information]
  • Atkinson, J., Nijhoff, F. (2010). A constructive approach to the soliton solutions of integrable quadrilateral Lattice equations. Communications in Mathematical Physics, 299, 283-304. [More Information]
  • Nijhoff, F., Atkinson, J. (2010). Elliptic N-soliton Solutions of ABS Lattice Equations. International Mathematics Research Notices, 20, 3837-3895. [More Information]
  • Atkinson, J. (2009). Linear quadrilateral lattice equations and multidimensional consistency. Journal of Physics A: Mathematical and Theoretical, 42(45), 454005-7 pp. [More Information]
  • Nijhoff, F., Atkinson, J., Hietarinta, J. (2009). Soliton solutions for ABS lattice equations: I. Cauchy matrix approach. Journal of Physics A: Mathematical and Theoretical, 42(40), 404005-34 pp. [More Information]
  • Atkinson, J., Kovalenko, I., Kuznetsov, N., Mykhalevych, K. (2008). A hypercube queueing loss model with customer-dependent service rates. European Journal of Operational Research, 191(1), 223-239. [More Information]
  • Atkinson, J. (2008). Backlund transformations for integrable lattice equations. Journal of Physics A: Mathematical and Theoretical, 41(13), 135202-38 pp. [More Information]
  • Atkinson, J., Hietarinta, J., Nijhoff, F. (2008). Soliton solutions for Q3. Journal of Physics A: Mathematical and Theoretical, 41(14), 142001-11 pp. [More Information]
  • Atkinson, J., Nijhoff, F. (2008). Solutions of Adler’s Lattice Equation Associated with 2-Cycles of the B¨acklund Transformation. Journal Of Nonlinear Mathematical Physics, 15(Supp. 3), 34-42.
  • Atkinson, J., Hietarinta, J., Nijhoff, F. (2007). Seed and soliton solutions for Adler’s lattice equation. Journal of Physics A: Mathematical and Theoretical, 40(1), F1-F8. [More Information]

2013

  • Atkinson, J., Joshi, N. (2013). Singular-Boundary Reductions of Type-Q ABS Equations. International Mathematics Research Notices, 7, 1451-1481. [More Information]

2012

  • Atkinson, J. (2012). A multidimensionally consistent version of Hirota's discrete KdV equation. Journal of Physics A: Mathematical and Theoretical, 45(22), 222001-1-222001-10. [More Information]
  • Atkinson, J., Lobb, S., Nijhoff, F. (2012). An integrable multicomponent quad-equation and its Lagrangian formulation. Theoretical and Mathematical Physics, 173(3), 1644-1653. [More Information]
  • Atkinson, J., Joshi, N. (2012). The Schwarzian variable associated with discrete KdV-type equations. Nonlinearity, 25(6), 1851-1866. [More Information]

2011

  • Atkinson, J. (2011). Singularities of Type-Q ABS Equations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7(article 073), 073-1-073-14. [More Information]

2010

  • Atkinson, J., Nijhoff, F. (2010). A constructive approach to the soliton solutions of integrable quadrilateral Lattice equations. Communications in Mathematical Physics, 299, 283-304. [More Information]
  • Nijhoff, F., Atkinson, J. (2010). Elliptic N-soliton Solutions of ABS Lattice Equations. International Mathematics Research Notices, 20, 3837-3895. [More Information]

2009

  • Atkinson, J. (2009). Linear quadrilateral lattice equations and multidimensional consistency. Journal of Physics A: Mathematical and Theoretical, 42(45), 454005-7 pp. [More Information]
  • Nijhoff, F., Atkinson, J., Hietarinta, J. (2009). Soliton solutions for ABS lattice equations: I. Cauchy matrix approach. Journal of Physics A: Mathematical and Theoretical, 42(40), 404005-34 pp. [More Information]

2008

  • Atkinson, J., Kovalenko, I., Kuznetsov, N., Mykhalevych, K. (2008). A hypercube queueing loss model with customer-dependent service rates. European Journal of Operational Research, 191(1), 223-239. [More Information]
  • Atkinson, J. (2008). Backlund transformations for integrable lattice equations. Journal of Physics A: Mathematical and Theoretical, 41(13), 135202-38 pp. [More Information]
  • Atkinson, J., Hietarinta, J., Nijhoff, F. (2008). Soliton solutions for Q3. Journal of Physics A: Mathematical and Theoretical, 41(14), 142001-11 pp. [More Information]
  • Atkinson, J., Nijhoff, F. (2008). Solutions of Adler’s Lattice Equation Associated with 2-Cycles of the B¨acklund Transformation. Journal Of Nonlinear Mathematical Physics, 15(Supp. 3), 34-42.

2007

  • Atkinson, J., Hietarinta, J., Nijhoff, F. (2007). Seed and soliton solutions for Adler’s lattice equation. Journal of Physics A: Mathematical and Theoretical, 40(1), F1-F8. [More Information]

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