Conservation Laws and Travelling Wave Solutions for Double Dispersion Equations in (1+1) and (2+1) Dimensions

Symmetry

MaríaLuz Gandarias¹  MaríaRosa Durán¹  ChaudryMasood Khalique² 

[1] Departamento de Matemáticas, Universidad de Cádiz, P.O. Box 40, 11510 Puerto Real, Cádiz, Spain;International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa;

关键词: conservation laws;    lie symmetries;    travelling wave solutions;   

DOI  :  10.3390/sym12060950

来源: DOAJ

【 摘 要 】

In this article, we investigate two types of double dispersion equations in two different dimensions, which arise in several physical applications. Double dispersion equations are derived to describe long nonlinear wave evolution in a thin hyperelastic rod. Firstly, we obtain conservation laws for both these equations. To do this, we employ the multiplier method, which is an efficient method to derive conservation laws as it does not require the PDEs to admit a variational principle. Secondly, we obtain travelling waves and line travelling waves for these two equations. In this process, the conservation laws are used to obtain a triple reduction. Finally, a line soliton solution is found for the double dispersion equation in two dimensions.

【 授权许可】

Unknown