Dr Peter H

Dr Peter H van der Kamp

Lecturer, Researcher

College of Science, Health and Engineering

School of Engineering and Mathematical Sciences

Department of Mathematics and Statistics

Physical Sciences 2, Room 319, Melbourne (Bundoora)

Qualifications

Doctorandus (Theoretical) Physics, PhD Mathematics.

Role

Academic

Membership of professional associations

The Australian Mathematical Society

Area of study

Mathematics and Statistics

Brief profile

Dr van der Kamp's main research interests lie in the field of integrable systems, a broad area at the boundary of  physics and mathematics. He is mainly concerned with algebraic and geometric properties of nonlinear differential equations and difference equations.

Research interests

Mathematical foundations of physics

- Integrable systems

Teaching units

MAT2LAL

MAT3AC

MAT4NT

MAT4TA

Recent publications

  • Integrable and superintegrable systems associated with multi-sums of products, Peter H. van der Kamp, Theodoros E. Kouloukas, G. R. W. Quispel, Dinh T. Tran and Pol Vanhaecke, Proc. R. Soc. A 470 (2014) 20140481.
  • Twisted reductions of integrable lattice equations, and their Lax representations, Christopher M. Ormerod, Peter H. van der Kamp, Jarmo Hietarinta, G. R. W. Quispel, Nonlinearity 27 (2014), 1367.
  • On the Fourier transform of the greatest common divisor, Peter H. van der Kamp, INTEGERS: 13 (2013) A24 (16pp).
  • Discrete Painlevé equations and their Lax pairs as reductions of integrable lattice equations, C.M. Ormerod, Peter H van der Kamp and G.R.W. Quispel, J. Phys. A: Math. Theor. 46 (2013) 095204 (22pp).
  • Integrability of reductions of the discrete Korteweg-De Vries and potential Korteweg-De Vries equations, A.N.W. Hone, P.H. van der Kamp, G.R.W. Quispel, and D. T. Tran, Proc R Soc A 469 (2013) 20120747.
  • Symbolic computation of Lax pairs of partial difference equations using consistency around the cube, T. Bridgman, W. Hereman, G. R. W. Quispel, and Peter H. van der Kamp, Foundations of Computational Mathematics 13 (2012) 517-544.
  • A novel n-th order difference equation that may be integrable, D.K. Demskoi, D.T. Tran, Peter H. van der Kamp and G.R.W Quispel, J. Phys. A: Math. Theor. 45 (2012) 135202.
  • Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps, D. Tran, Peter H. van der Kamp, G.R.W. Quispel, J. Phys. A 44 (2011) 295206.
  • Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm, Paul E. Spicer, Frank W. Nijhoff, Peter H. van der Kamp, Nonlinearity 24 (2011) 2229-2263.
  • Growth of degrees of integrable mappings, Peter H. van der Kamp, Journal of Difference Equations and Applications 18 (2011) 447460.
  • The staircase method; integrals for periodic reductions of integrable lattice equations, Peter H. van der Kamp and G.R.W. Quispel, J. Phys. A: Math. Theor. 43 (2010) 465207 (34pp).
  • Sufficient number of integrals for the pth order Lyness equation, Dinh T Tran, Peter H. van der Kamp, G.R.W. Quispel, J. Phys. A: Math. Theor. 43 (2010) 302001.
  • Global classification of 2-component approximately integrable evolution equations, Peter H. van der Kamp, Foundations of Computational Mathematics 9 (2009), 559–597.
  • Initial value problems for lattice equation, Peter H. van der Kamp, J. Phys. A: Math. Theor. 42 (2009) 404019.
  • Closed-form expressions for integrals of traveling wave reductions of integrable lattice equations, Dinh T. Tran, Peter H. van der Kamp, G.R.W. Quispel, J. Phys. A: Math. Theor. 42 (2009) 225201 (20pp).