3 citations · 4 across the 5 of their papers we have counts for
5 papers
Lattice KP type equations arising from eigenfunctions and Dbar problem
Leilei Shi, Peter van der Kamp, Cheng Zhang +1
In this paper, we construct the lattice Kadomtsev-Petviashvili (KP) type eigenfunction equations. A homogeneous nonlocal problem is considered, from which we are a…
Liouville integrable Lotka-Volterra systems
Peter H. van der Kamp, David I. McLaren, G. R. W. Quispel
We present homogeneous -parameter families of Liouville integrable - and -dimensional Lotka-Volt…
Trees and superintegrable Lotka-Volterra families
Peter H. van der Kamp, G. R. W. Quispel, D. I. McLaren
To any tree on vertices we associate an -dimensional Lotka-Volterra system with parameters and, for generic values of the parameters, prove it is superintegrable, i.e…
Measure preservation and integrals for Lotka--Volterra tree-systems and their Kahan discretisation
Peter H. van der Kamp, Robert I. McLachlan, David I. McLaren +1
We show that any Lotka--Volterra tree-system associated with an -vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also…
New Class of Integrable Maps of the Plane: Manin Transformations with Involution Curves
Peter H. van der Kamp
For cubic pencils we define the notion of an involution curve. This is a curve which intersects each curve of the pencil in exactly one non-base point of the pencil. Involution cur…