Traveling Wave Solutions of the Burgers – Gardner Equation with a Nonlinear Source

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-12-30 DOI:10.1134/S1560354725560047

Nikolay A. Kudryashov

引用次数: 0

Abstract

The Burgers – Gardner equation with a nonlinear source is considered. The Cauchy problem for this equation cannot be solved by the inverse scattering transform and we look for the traveling wave solutions. The Painlevé test is used to find constraints on the parameters of the equation for its integrability. The first integral of the nonlinear ordinary differential equation is obtained taking into account the results of the Painlevé test. The first integral thus found is used to obtain the general solution of the equation. Some exact solutions are found by means of the simplest equation method.

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非线性源下Burgers - Gardner方程的行波解

考虑具有非线性源的Burgers - Gardner方程。该方程的柯西问题不能用逆散射变换求解，我们寻找行波解。用painlevel检验寻找方程可积性参数的约束条件。考虑painlevlevw检验的结果，得到了非线性常微分方程的第一个积分。这样得到的第一个积分用于得到方程的通解。用最简方程法求出了若干精确解。

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

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.