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运用广义(G'/G)展开法的新方法求解KP-BBM方程的精确行波解

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

作者信息

Alam Md Nur, Akbar M Ali

机构信息

Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh.

出版信息

Springerplus. 2013 Nov 19;2:617. doi: 10.1186/2193-1801-2-617. eCollection 2013.

DOI:10.1186/2193-1801-2-617
PMID:24307985
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC3843771/
Abstract

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

摘要

广义(G'/G)展开法的新方法是一种在科学、工程和数学物理领域中寻找非线性演化方程(NLEEs)精确行波解的有效且强大的数学工具。在本文中，广义(G'/G)展开法的新方法被应用于构造Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM)方程的行波解。这些解以双曲函数、三角函数和有理函数表示。通过该方法，我们找到了上述方程的一些新的行波解。

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Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis.研究波解与非线性影响：用分岔分析研究 KP-BBM 模型的综合分析。
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A new implementation of a novel analytical method for finding the analytical solutions of the (2+1)-dimensional KP-BBM equation.一种用于求解(2 + 1)维KP - BBM方程解析解的新型分析方法的新实现。
Heliyon. 2023 Apr 24;9(5):e15690. doi: 10.1016/j.heliyon.2023.e15690. eCollection 2023 May.
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The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.基于对称方法的(2 + 1)维KP方程的精确解和近似解析解。
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