Solution of double and triple sine-Gordon equations

IF 1.1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-09-26 DOI:10.1134/S0040577925090089

Yu. V. Pavlov

引用次数: 0

Abstract

A method for solving the double and triple sine-Gordon equations with first derivatives is presented. The search for solutions is similar to the search for functionally invariant solutions of the multidimensional wave equation. The solvability of the resulting system of equations is analyzed. The solution of the double sine-Gordon equation is obtained in explicit form by inverting the elliptic integral. The solution of the triple sine-Gordon equation requires inversion of the ultra-elliptic integral in the general case.

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二重和三重正弦戈登方程的解

给出了一阶导数的双重和三重正弦戈登方程的一种求解方法。寻找解类似于寻找多维波动方程的函数不变解。分析了所得方程组的可解性。通过对椭圆积分进行反求，得到了二重正弦-戈登方程的显式解。在一般情况下，三重正弦-戈登方程的求解需要对超椭圆积分进行反演。

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

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.