53 citations · 196 across the 27 of their papers we have counts for
4 papers · 1 filter
Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps
Dinh T. Tran, P. H. van der Kamp, G. R. W. Quispel
Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korte…
Growth of degrees of integrable mappings
Peter H. van der Kamp
We study mappings obtained as s-periodic reductions of the lattice Korteweg-De Vries equation. For small s=(s1,s2) we establish upper bounds on the growth of the degree of the nume…
The staircase method: integrals for periodic reductions of integrable lattice equations
Peter H. van der Kamp, G. R. W. Quispel
We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partia…
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
Paul E. Spicer, Frank W. Nijhoff, Peter H. van der Kamp
The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adj…