53 citations · 196 across the 27 of their papers we have counts for
32 papers
Hypergraphs and Lotka-Volterra systems with linear Darboux polynomials
Peter H. van der Kamp
We associate parametric classes of -component Lotka-Volterra systems which admit additional linear Darboux polynomials, with admissible loopless hypergraphs of order and…
On trilinear and quadrilinear equations associated with the lattice Gel'fand-Dikii hierarchy
P. H. van der Kamp, F. W. Nijhoff, D. I. McLaren +1
Introduced in 2012, by Zhang, Zhao, and Nijhoff, the trilinear Boussinesq equation is the natural form of the equation for the -function of the lattice Boussinesq system. In thi…
On a quadratic Poisson algebra and integrable Lotka-Volterra systems with solutions in terms of Lambert's W function
Peter H. van der Kamp, D. I. McLaren, G. R. W. Quispel
We study a class of integrable nonhomogeneous Lotka-Volterra systems whose quadratic terms are defined by an antisymmetric matrix and whose linear terms consist of three blocks. We…
Linear Darboux polynomials for Lotka-Volterra systems, trees and superintegrable families
G. R. W. Quispel, Benjamin K. Tapley, D. I. McLaren +1
We present a method to construct superintegrable -component Lotka-Volterra systems with parameters. We apply the method to Lotka-Volterra systems with components for…
Integrability of auto-Bäcklund transformations,and solutions of a torqued ABS equation
Xueli Wei, Peter H. van der Kamp, Da-jun Zhang
An auto-Bäcklund transformation for the quad equation is considered as a discrete equation, called , which is a so called torqued version of $\mathrm…
From auto-Bäcklund transformations to auto-Bäcklund transformations, and torqued ABS equations
Dan-da Zhang, Da-jun Zhang, Peter H. van der Kamp
We provide a method which takes an auto-Bäcklund transformation (auto-BT) and produces another auto-BT for a different equation. We apply the method to the natural auto-BTs for the…