53 citations · 187 across the 29 of their papers we have counts for
32 papers
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…
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…
Birational maps from polarization and the preservation of measure and integrals
Robert I McLachlan, David I McLaren, G R W Quispel
The main result of this paper is the discretization of Hamiltonian systems of the form , where is a constant symmetric matrix and $W\colon\mathbb{R}^n…