Zobrazeno 1 - 10
of 555
pro vyhledávání: '"McLaren, D. A."'
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 provide the Poisson algebra of their Darboux polynomials, and prove a
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
To any tree on $n$ vertices we associate an $n$-dimensional Lotka-Volterra system with $3n-2$ parameters and, for generic values of the parameters, prove it is superintegrable, i.e. it admits $n-1$ functionally independent integrals. We also show how
Externí odkaz:
http://arxiv.org/abs/2311.15169
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 show that some hard to detect properties of quadratic ODEs (eg certain preserved integrals and measures) can be deduced more or less algorithmically from their Kahan discretization, using Darboux Polynomials (DPs). Somewhat similar results hold fo
Externí odkaz:
http://arxiv.org/abs/2104.05951
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
Autor:
Celledoni, E, Evripidou, C, McLaren, D I, Owren, B, Quispel, G R W, Tapley, B K, van der Kamp, P H
In this Letter we propose a systematic approach for detecting and calculating preserved measures and integrals of a rational map. The approach is based on the use of cofactors and Discrete Darboux Polynomials and relies on the use of symbolic algebra
Externí odkaz:
http://arxiv.org/abs/1902.04715
Discrete gradient methods are well-known methods of Geometric Numerical Integration, which preserve the dissipation of gradient systems. The preservation of the dissipation of a system is an important feature in numerous image processing tasks. We pr
Externí odkaz:
http://arxiv.org/abs/1603.07515
Publikováno v:
Discrete Contin. Dyn. Syst., 35 (5), 2079-2098, 2015
In this paper we study linear projection methods for approximating the solution and simultaneously preserving first integrals of autonomous ordinary differential equations. We show that (linear) projection methods are a subset of discrete gradient me
Externí odkaz:
http://arxiv.org/abs/1302.2713