Publications

Peter H. van der Kamp


Publications

Publications

Thesis

    1. P.H. van der Kamp, Integrable Evolution Equations: a Diophantine Approach, PhD thesis, vrije Universiteit, Amsterdam.

Book chapter

    1. P.H. van der Kamp and Jan A. Sanders and J. Top, Integrable systems and number theory, chapter 8 in Differential Equations and the Stokes Phenomenon, 2002 World Scientific Publishing, 171-201.

Proceedings

  1. P.H. van der Kamp, The use of p-adic numbers in calculating symmetries of evolution equations, proceedings ‘Symmetry in Nonlinear Mathematical Physics 2001’ (2002) 151-155.

  2. Chris Budd et al., Hanging a Carillon in a Broeksystem, Proceedings Fourty-Fifth European Study Group with Industry (2004) 73–90.

    1. P.H. van der Kamp, Towards global classifications: a Diophantine approach, proceedings ‘Symmetry and Perturbation Theory 2007’ (2007) 278-279. Erratum

    2. O. Rojas, P.H. van der Kamp and G.R.W. Quispel, Lax representation for integrable O∆Es, proceedings ‘Symmetry and Perturbation Theory 2007’ (2007) 271-272.

    Papers

    1. P.H. van der Kamp and Jan A. Sanders, On Testing Integrability, J Nonlinear Math. Phys. 8 (2001) 561-574.

    2. P.H. van der Kamp and Jan A. Sanders, Almost Integrable Evolution Equations, Selecta Math. (N.S.) 8 (2002) 705-719.
    3. P.H. van der Kamp, On proving integrability, Inverse Probl. 18 (2002) 405-414.
    4. P.H. van der Kamp, Classification of Integrable B-equations, J. Differ. Equations 202 (2004) 256-283.
    5. E.L. Mansfield and P.H. van der Kamp, Evolution of curvature invariants and lifting integrability, J. Geom. Phys. 56 (2006) 1294-1325.
    6. P.H. van der Kamp, O. Rojas and G.R.W. Quispel, Closed-form expressions for integrals of mKdV and sine-Gordon maps, J. Phys A: Math Gen. 40 (2007) 12789-12798.
    7. D.T. Tran, P.H. van der Kamp and G.R.W. Quispel, Closed-form expressions for integrals of traveling wave reductions of integrable lattice equations, J. Phys. A: Math. Theor. 42 (2009) 225201.
    8. P.H. van der Kamp, Initial value problems for lattice equations, J. Phys. A: Math. Theor. 42 (2009) 404019.
    9. P.H. van der Kamp, Global classification of 2-component approximately integrable evolution equations, Found. Comput. Math. 9 (2009) 559-597.
    10. D.T. Tran, P.H. van der Kamp and G.R.W. Quispel, Sufficient number of integrals for the pth order Lyness equation, J. Phys. A: Math. Theor. 43 (2010) 302001.
    11. P.H. van der Kamp and G.R.W. Quispel, The staircase method: integrals for periodic reductions of integrable lattice equations, J. Phys. A: Math. Theor. 43 (2010) 465207.
    12. P.H. van der Kamp, Growth of degrees of integrable mappings, J. Differ. Equ. Appl. 18 (2011) 447-460.
    13. P.E. Spicer, F.W. Nijhoff and P.H. van der Kamp, Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm, Nonlinearity 24 (2011) 2229-2263.
    14. D. Tran, P.H. van der Kamp and G.R.W. Quispel, Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps, J. Phys. A 44 (2011) 295206.
    15. D.K. Demskoi, D.T. Tran, P.H. van der Kamp and G.R.W Quispel, A novel nth order difference equation that may be integrable, J. Phys. A: Math. Theor. 45 (2012) 135202.
    16. T. Bridgman, W. Hereman, G.R.W. Quispel and P.H. van der Kamp, Symbolic computation of Lax pairs of partial difference equations using consistency around the cube, Found. Comput. Math. 13 (2013) 517-544.
    17. A.N.W. Hone, P.H. van der Kamp, G.R.W. Quispel and D.T. Tran, Integrability of reductions of the discrete Korteweg-De Vries and potential Korteweg-De Vries equations, Proc R Soc A 469 (2013) 20120747.
    18. C.M. Ormerod, P.H. van der Kamp and G.R.W. Quispel, Discrete Painleve equations and their Lax pairs as reductions of integrable lattice equations, J. Phys. A: Math. Theor. 46 (2013) 095204 (22pp).
    19. P.H. van der Kamp, On the Fourier transform of the greatest common divisor, INTEGERS 13 (2013) A24 (16pp).
    20. C.M. Ormerod, P.H. van der Kamp, J. Hietarinta and G.R.W. Quispel, Twisted reductions of integrable lattice equations, and their Lax representations, Nonlinearity 27 (2014) 1367-1390.
    21. P.H. van der Kamp, T.E. Kouloukas, G.R.W. Quispel, D.T. Tran and P. Vanhaecke, Integrable and superintegrable systems associated with multi-sums of products, Proc. R. Soc. A 470 (2014) 20140481.
    22. P.H. van der Kamp, Initial value problems for quad equations, J. Phys. A: Math. Theor. 48 (2015) 065204.
    23. P.H. van der Kamp, Somos-4 and Somos-5 are arithmetic divisibility sequences, J. Difference Equ. Appl. 22 (2016) 570-580.
    24. Dinh T. Tran, Peter H. van der Kamp, and G.R.W. Quispel, Poisson brackets of mappings obtained as (q,−p) reductions of lattice equations, Regular and Chaotic Dynamics 21 (2016) 682-696.
    25. K. Hamad and P.H. van der Kamp, From discrete integrable equations to Laurent recurrences, J. Difference Equ. Appl. 22 (2016) 789-816.
    26. K. Hamad, A.N.W. Hone, P.H. van der Kamp and G.R.W. Quispel, QRT maps and related Laurent systems, Adv. Appl. Math. 96 (2018) 216-248.
    27. C.A. Evripidou, P.H. van der Kamp and C. Zhang, Dressing the Dressing Chain, SIGMA 14 (2018) 059, 14 pp.
    28. P.H. van der Kamp, G.R.W Quispel and D.-J. Zhang, Duality for discrete integrable systems II, J. Phys. A: Math. Theor. 51 (2018) 365202.
    29. E. Celledoni, C. Evripidou, D.I. McLaren, B. Owren, G.R.W. Quispel, B.K. Tapley and P.H. van der Kamp, Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps, J. Phys. A: Math. Theor. 52 (2019) 31LT01 (11pp).
    30. P.H. van der Kamp, E. Celledoni, R.I. McLachlan, D.I. McLaren, B. Owren, G.R.W. Quispel, Three classes of quadratic vector fields for which the Kahan discretization is the root of a generalised Manin transformation, J. Phys. A: Math. Theor. 52 (2019) 045204 (10pp).
    31. J.M. Tuwankotta, P.H. van der Kamp, G.R.W. Quispel and K.V.I. Saputra, Generating a chain of maps which preserve the same integral as a given map, Phys. Scr. 94 (2019) 125207 (11pp).
    32. J. Moorfield, S. Wang, W. Yang, A. Bedari, P.H. van der Kamp, A Möbius transformation based model for fingerprint minutiae variations, Pattern Recognition 98 (2020) 107054.
    33. D.D. Zhang, P.H. van der Kamp, D.-J. Zhang, Multi-component extension of CAC systems, SIGMA 16 (2020), 060, 30 pages.
    34. G.R.W. Quispel, D.I. McLaren, P.H. van der Kamp, A novel 8-parameter integrable map in R4, J. Phys. A: Math. Theor. 53 (2020) 40LT01 (6pp).
    35. P.H. van der Kamp, D.I. McLaren, G.R.W. Quispel, Homogeneous Darboux polynomials and generalising integrable ODE systems, J. Comput. Dyn. 8(1) (2021) 1-8.
    36. P.H. van der Kamp, D.I. McLaren and G.R.W. Quispel, Generalised Manin transformations and QRT maps, J. Comput. Dyn. 8(2) (2021) 183-211.
    37. X. Wei, P.H. van der Kamp, D.J. Zhang, Integrability of auto-Bäcklund transformations and solutions of a torqued ABS equation, Comm. Theor. Phys. 73 (2021) 075005 (5pp).
    38. P.H. van der Kamp, A new class of integrable maps of the plane: Manin transformations with involution curves, SIGMA 17 (2021), 067, 14 pages.

      1. V. Caudrelier, P.H. van der Kamp, C. Zhang, Integrable boundary conditions for quad equations, open boundary reductions and integrable mappings, Int. Math. Res. Not. 00, No. 0, pp. 1–44, https://doi.org/10.1093/imrn/rnab188.

      2. D.D Zhang, D.J. Zhang, P.H. van der Kamp, From auto-Bäcklund transformations to auto-Bäcklund transformations, and torqued ABS equations, Math Phys Anal Geom (2021) 24:33.


      Preprints

        1. P.H. van der Kamp, Symmetry condition in terms of Lie brackets, arXiv:0802.1954v2 [nlin.SI].
        2. P.H. van der Kamp, D.-J. Zhang, G.R.W. Quispel, On the relation between the dual AKP equation and an equation by King and Schief, and its N-soliton solution, arXiv:1912.02299 [nlin.SI].