Singularity Confinement and Proliferation of Tau Functions for a General Differential-Difference Sawada-Kotera Equation

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-09-21 DOI:10.1007/s11040-025-09524-0

A. Marin, A. S. Carstea

引用次数: 0

Abstract

By blending Painlevé property with singularity confinement for a general arbitrary order Sawada-Kotera differential-difference equation, we find a proliferation of “tau-functions” (coming from confined patterns). However, only one of these function enters into the Hirota bilinear form (the others give multi-linear expressions) but it has specific relations with all others. We also discuss two modifications of the Sawada-Kotera equation. Fully discretizations and the express method for computing algebraic entropy are discussed.

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一般微分-差分Sawada-Kotera方程的Tau函数的奇异约束和扩散

通过将painlev性质与一般任意阶Sawada-Kotera微分-差分方程的奇异约束相结合，我们发现了“tau函数”的扩散（来自受限模式）。然而，这些函数中只有一个进入Hirota双线性形式（其他函数给出多线性表达式），但它与所有其他函数都有特定的关系。我们还讨论了Sawada-Kotera方程的两种修正。讨论了计算代数熵的完全离散化和表示方法。

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

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.