Non-Existence of S-Integrable Three-Point Partial Difference Equations in the Lattice Plane

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-11-01 DOI:10.3842/sigma.2023.084

Decio Levi, Miguel A. Rodríguez

引用次数: 0

Abstract

Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to Yamilov's theorem. We shall apply this result to a class of differential-difference equations obtained as partial continuous limits of 3-points difference equations in the plane and conclude that they cannot be integrable.

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格平面上s可积三点偏差分方程的不存在性

根据亚米洛夫定理，确定一个(1+1)-微分-差分方程是否可积(在具有无限多个对称的意义上)可以归结为研究方程对晶格点的依赖关系。我们将这一结果应用于作为三点差分方程在平面上的部分连续极限而得到的一类微分-差分方程，并得出它们不可积的结论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.