On a class of exact solutions of the Ishimori equation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI:10.1016/j.physd.2025.134746

Rustem N. Garifullin, Ismagil T. Habibullin

引用次数: 0

Abstract

In this paper, a class of particular solutions of the Ishimori equation is found. This equation is known as the spatially two-dimensional version of the Heisenberg equation, which has important applications in the theory of ferromagnets. It is shown that the two-dimensional Toda-type lattice found earlier by Ferapontov, Shabat and Yamilov is a dressing chain for this equation. Using the integrable reductions of the dressing chain, the authors found an essentially new class of solutions to the Ishimori equation.

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石森方程的一类精确解

本文给出了Ishimori方程的一类特解。这个方程被称为海森堡方程的空间二维版本，它在铁磁体理论中有重要的应用。证明了Ferapontov， Shabat和Yamilov早先发现的二维toda型晶格是该方程的修饰链。利用修整链的可积约化，作者发现了Ishimori方程实质上的一类新的解。

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

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.