53 citations · 187 across the 29 of their papers we have counts for
4 papers · 1 filter
Analogues of Kahan's method for higher order equations of higher degree
A. N. W. Hone, G. R. W. Quispel
Kahan introduced an explicit method of discretization for systems of first order differential equations with nonlinearities of degree at most two (quadratic vector fields). Kahan's…
On the relation between the dual AKP equation and an equation by King and Schief, and its N-soliton solution
Peter H. van der Kamp, Da-jun Zhang, G. R. W. Quispel
The Dual of the lattice AKP (DAKP) equation [P.H. van der Kamp et al., J. Phys. A 51, 365202 (2018)] is equivalent to a 14-point equation related to the lattice BKP equation, found…
Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
E Celledoni, C Evripidou, D I McLaren +4
In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and…
Generating a chain of maps which preserve the same integral as a given map
J. M. Tuwankotta, P. H. van der Kamp, G. R. W. Quispel +1
We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with…