重新审视阿德勒-博本科-苏里斯晶格方程和晶格布辛斯方程的解法

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-06-25 DOI:10.1134/S0040577924060059

Song-lin Zhao, Ke Yan, Ying-ying Sun

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引用次数: 0

摘要

摘要利用考奇矩阵方法重新考虑了除\(Q4\)之外的所有阿德勒-博本科-苏里斯方程和几个布辛斯方程的解。通过引入一个 "假的 "非自主平面波因子，我们得出了目标晶格方程的孤子解、振荡解和半振荡解。与传统的孤子解不同，振荡解在\(\mathbb{Z}^2\)上的所有基本四边形上都取恒定值，这表明了一种周期性结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations

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Revisiting solutions of the Adler–Bobenko–Suris lattice equations and lattice Boussinesq-type equations

Solutions of all Adler–Bobenko–Suris equations except \(Q4\), and of several lattice Boussinesq-type equations are reconsidered by using the Cauchy matrix approach. By introducing a “fake” nonautonomous plane-wave factor, we derive soliton solutions, oscillatory solutions, and semi-oscillatory solutions of the target lattice equations. Unlike the conventional soliton solutions, the oscillatory solutions take constant values on all elementary quadrilaterals on \(\mathbb{Z}^2\), which demonstrates a periodic structure.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.