53 citations · 187 across the 29 of their papers we have counts for
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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…
Subalgebras of integrals, commutants, and superintegrable deformations of Lotka-Volterra systems
Ian Marquette, Peter H. van der Kamp, G. R. W. Quispel
We consider the Lie-algebraic notion of commutant in the setting of Poisson algebra. This provides a framework for deforming Hamiltonian differential equations. By taking a subalge…
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…
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…
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…
A novel 8-parameter integrable map in
G R W Quispel, D I McLaren, P H van der Kamp
We present a novel 8-parameter integrable map in . The map is measure-preserving and possesses two functionally independent 2-integrals, as well as a measure-preservi…