Symmetric structures and dynamic analysis of a (2+1)-dimensional generalized Benny-Luke equation

IF 2.6 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica Scripta Pub Date : 2024-09-15 DOI:10.1088/1402-4896/ad7538

Jie Sun, Qiulan Zhao and Xinyue Li

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Abstract

We study the symmetric structures and dynamic analysis of a (2 + 1)-dimensional generalized Benny-Luke (GBL) equation based on the Lie symmetry method, the GBL equation is an important non-integrable model of water waves. Specifically, we construct multiple exact solutions of the GBL equation and obtain its nonlocally related systems. Firstly, the Lie point symmetries and conservation laws of the GBL equation are computed, and then we get the reduced ordinary differential equation from one of the conservation laws. Multiple methods, for example, the dynamical systems method, the power series method, the homogeneous balancing method and generalized variable separation method, are used to solve the ordinary differential equation and abundant exact solutions of the GBL equation are got. Finally, we extend these exact solutions by discrete symmetries, and give three-dimensional graphs of partial exact solutions. In addition, we construct the nonlocally related PDE systems, which contains the potential systems from the conservation laws and an inverse system from a Lie point symmetry of the GBL equation. These findings reveal the dynamical behavior behind the GBL equation and broaden the range of nonlinear water wave model solutions.

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(2+1)维广义班尼-卢克方程的对称结构和动态分析

我们基于Lie对称方法研究了(2 + 1)维广义Benny-Luke（GBL）方程的对称结构和动力学分析，GBL方程是一个重要的水波非可积分模型。具体而言，我们构建了 GBL 方程的多个精确解，并得到其非局部相关系统。首先计算 GBL 方程的列点对称性和守恒律，然后从其中一个守恒律得到还原常微分方程。然后用多种方法，如动力系统法、幂级数法、均质平衡法和广义变量分离法来求解常微分方程，得到 GBL 方程丰富的精确解。最后，我们通过离散对称性扩展了这些精确解，并给出了部分精确解的三维图形。此外，我们还构建了非局部相关的 PDE 系统，其中包含来自守恒定律的势系统和来自 GBL 方程的 Lie 点对称性的逆系统。这些发现揭示了 GBL 方程背后的动力学行为，拓宽了非线性水波模型解的范围。

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 Scripta 物理-物理：综合

CiteScore

3.70

自引率

3.40%

发文量

782

审稿时长

4.5 months

期刊介绍： Physica Scripta is an international journal for original research in any branch of experimental and theoretical physics. Articles will be considered in any of the following topics, and interdisciplinary topics involving physics are also welcomed: -Atomic, molecular and optical physics- Plasma physics- Condensed matter physics- Mathematical physics- Astrophysics- High energy physics- Nuclear physics- Nonlinear physics. The journal aims to increase the visibility and accessibility of research to the wider physical sciences community. Articles on topics of broad interest are encouraged and submissions in more specialist fields should endeavour to include reference to the wider context of their research in the introduction.