From Auto-Bäcklund Transformations to Auto-Bäcklund Transformations, and Torqued ABS Equations

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2021-09-23 DOI:10.1007/s11040-021-09406-1

Dan-da Zhang, Da-jun Zhang, Peter H. van der Kamp

引用次数: 4

Abstract

We provide a method which from a given auto-Bäcklund transformation (auto-BT) 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 equations and explains the origin of each auto-BT listed in Atkinson (J. Phys. A: Math. Theor. 41(8pp), 135202, 2008). The method is also applied to non-natural auto-BTs for ABS equations, which yields 3D consistent cubes which have not been found in Boll (J. Nonl. Math. Phys. 18, 337–365, 2011), and to a multi-quadratic ABS* equation giving rise to a multi-quartic equation.

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从Auto-Bäcklund变换到Auto-Bäcklund变换，以及扭力ABS方程

我们提供了一种方法，从一个给定的auto-Bäcklund变换(auto-BT)产生另一个不同方程的auto-BT。我们将该方法应用于ABS四元方程的自然自动bt，从而产生ABS方程的扭矩版本，并解释了Atkinson (J. Phys)中列出的每个自动bt的起源。答:数学。理论。41(8页)，135202,2008)。该方法也适用于ABS方程的非天然自动bt，产生在Boll (J. Nonl)中未发现的3D一致立方体。数学。物理学报，18,337-365,2011)，并得到一个多二次ABS*方程，从而得到一个多四次方程。

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.