Zobrazeno 1 - 10
of 76
pro vyhledávání: '"van der Kamp, P. H."'
We study a class of integrable nonhomogeneous Lotka-Volterra systems whose quadratic terms defined by an antisymmetric matrix and whose linear terms consist of three blocks. We provide the Poisson algebra of their Darboux polynomials, and prove a con
Externí odkaz:
http://arxiv.org/abs/2408.14720
Introduced in 2012, by Zhang, Zhao, and Nijhoff, the trilinear Boussinesq equation is the natural form of the equation for the $\tau$-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontr
Externí odkaz:
http://arxiv.org/abs/2407.11175
Publikováno v:
Journal of Computational Dynamics, 2024
We show that any Lotka--Volterra tree-system associated with an $n$-vertex tree, as introduced in Quispel et al., J. Phys. A 56 (2023) 315201, preserves a rational measure. We also prove that the Kahan discretisation of these tree-systems factorises
Externí odkaz:
http://arxiv.org/abs/2309.05979
We present a method to construct superintegrable $n$-component Lotka-Volterra systems with $3n-2$ parameters. We apply the method to Lotka-Volterra systems with $n$ components for $1 < n < 6$, and present several $n$-dimensional superintegrable famil
Externí odkaz:
http://arxiv.org/abs/2303.00229
We provide a method which takes an auto-B\"acklund transformation (auto-BT) and produces another auto-BT for a different equation. We apply the method to the natural auto-BTs for the ABS quad equations, which gives rise to torqued versions of ABS equ
Externí odkaz:
http://arxiv.org/abs/2102.11668
An auto-B\"acklund transformation for the quad equation $\mathrm{Q1}_1$ is considered as a discrete equation, called $\mathrm{H2}^a$, which is a so called torqued version of $\mathrm{H2}$. The equations $\mathrm{H2}^a$ and $\mathrm{Q1}_1$ compose a c
Externí odkaz:
http://arxiv.org/abs/2102.12062
Autor:
van der Kamp, Peter H.
Publikováno v:
SIGMA 17 (2021), 067, 14 pages
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 curves can be used to construct integrable maps of the plane which leave
Externí odkaz:
http://arxiv.org/abs/2009.09854
In the context of integrable partial difference equations on quad-graphs, we introduce the notion of open boundary reductions as a new means to construct discrete integrable mappings and their invariants. This represents an alternative to the well-kn
Externí odkaz:
http://arxiv.org/abs/2009.00412
We present a novel 8-parameter integrable map in $\mathbb{R}^4$. The map is measure-preserving and possesses two functionally independent 2-integrals, as well as a measure-preserving 2-symmetry.
Externí odkaz:
http://arxiv.org/abs/2003.05588
We show that any system of ODEs can be modified whilst preserving its homogeneous Darboux polynomials. We employ the result to generalise a hierarchy of integrable Lotka-Volterra systems.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2002.08548