Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

He Yinghui

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Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

机译：高维浅水波方程的Lie对称性分析和新的精确解

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In our work, a higher-dimensional shallow water wave equation, which can be reduced to the potential KdV equation, is discussed. By using the Lie symmetry analysis, all of the geometric vector fields of the equation are obtained; the symmetry reductions are also presented. Some new nonlinear wave solutions, involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function, and trigonometric function are obtained. Our work extends pioneer results.

机译：在我们的工作中，讨论了可以简化为势KdV方程的高维浅水波方程。通过使用李对称性分析，可以获得方程的所有几何矢量场。还介绍了对称性的减少。得到了一些新的非线性波解，它们涉及可微分的任意函数，分别由雅可比椭圆函数，韦斯特拉斯椭圆函数，双曲函数和三角函数表示。我们的工作扩展了先锋成果。

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《Mathematical Problems in Engineering》 |2015年第12期|426363.1-426363.10|共10页
作者
He Yinghui;
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Honghe Univ, Dept Math, Mengzi 661100, Yunnan, Peoples R China.;

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1. Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation [J] . YinghuiHe Mathematical Problems in Engineering: Theory, Methods and Applications . 2015,第5期

机译：高维浅水波方程的Lie对称性分析和新的精确解
2. Lie Symmetries and Exact Solutions of Shallow Water Equations with Variable Bottom [J] . Pandey Manoj International journal of nonlinear sciences and numerical simulation . 2015,第7a8期

机译：底部可变浅水方程的Lie对称性和精确解
3. Some new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation by Lie symmetry approach [J] . Kumar Dharmendra, Kumar Sachin Computers & mathematics with applications . 2019,第3期

机译：用Lie对称方法求解（3 + 1）维广义浅水波方程的一些新的周期孤立波解
4. Lie Symmetry Analysis and Exact Solutions for the Coupled Kuramoto-Sivashinsky Equations [C] . Yan Fang, Hua Cuncai, Liu Haihong, 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications . 2011

机译：耦合的Kuramoto-Sivashinsky方程的Lie对称性分析和精确解
5. Multi-Soliton solutions to a model equation for shallow water waves. [D] . Qiao, Zhijiang. 2010

机译：浅水波模型方程的多孤子解。
6. Symmetry reduction and exact solutions of two higher-dimensional nonlinear evolution equations [O] . Yongyi Gu, Jianming Qi -1

机译：两个高维非线性发展方程的对称约化和精确解
7. Symmetry Reductions and Exact Solutions of Shallow Water Wave Equations [O] . Clarkson, Peter A., Mansfield, Elizabeth L. 1994

机译：浅水波方程的对称约化与精确解

Lie Symmetry Analysis and New Exact Solutions for a Higher-Dimensional Shallow Water Wave Equation

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