Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation

Feng Zhang,Yuru Hu,Xiangpeng Xin,Stephen C Anco

doi:10.1155/2021/6227384

Feng Zhang, Yuru Hu + Show 2 more

Open Access

https://doi.org/10.1155/2021/6227384

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Abstract

In this article, we study the generalized ( 2 + 1 )-dimensional variable-coefficients Boiti-Leon-Pempinelli (vcBLP) equation. Using Lie’s invariance infinitesimal criterion, equivalence transformations and differential invariants are derived. Applying differential invariants to construct an explicit transformation that makes vcBLP transform to the constant coefficient form, then transform to the well-known Burgers equation. The infinitesimal generators of vcBLP are obtained using the Lie group method; then, the optimal system of one-dimensional subalgebras is determined. According to the optimal system, the ( 1 + 1 )-dimensional reduced partial differential equations (PDEs) are obtained by similarity reductions. Through G ′ / G -expansion method leads to exact solutions of vcBLP and plots the corresponding 3-dimensional figures. Subsequently, the conservation laws of vcBLP are determined using the multiplier method.

Highlights

Nonlinear issues are widespread in some natural disciplines, and many difficult problems in some disciplines can be reduced to solving a certain partial differential equations (PDEs) or investigating some properties of a PDE [1, 2]
We can find some periodic solutions and soliton solutions of variable-coefficients Boiti-Leon-Pempinelli (vcBLP) obtained with the homogeneous balance method in [11], and the conservation laws for the constant coefficients BLP were discussed in [9]
Based on the above facts, we use differential invariants to give the transformation of vcBLP to its constant coefficient form

Summary

Introduction

Nonlinear issues are widespread in some natural disciplines, and many difficult problems in some disciplines can be reduced to solving a certain PDE or investigating some properties of a PDE [1, 2]. We focus on the generalized (2 + 1)-dimensional Boiti-Leon-Pempinelli equation with time-part variable coefficients as It represents the development of the components in the horizontal velocity in the x and y directions when the water wave propagates in a channel of unchanging depth and infinitely small width [9].

Equivalence Transformations and Differential Invariants of vcBLP

Lie Classical Symmetry Analysis of vcBLP

Exact Solutions of vcBLP

Conservation Laws of vcBLP

Conclusions of This Article