On the classical and nonclassical symmetries of a generalized Gardner equation

Applied Mathematics and Nonlinear Sciences

卷:1

de la Rosa R.¹  Bruzón M.S.¹ 

[1] Departamento de Matemáticas, Universidad de Cádiz, P.O. Box 40, Puerto Real 11510, CádizSpain;

关键词: partial differential equations;    symmetries;    exact solutions;    35c07;    35q35;    35q40;    76m60;   

DOI  :  10.21042/AMNS.2016.1.00021

来源: DOAJ

【 摘 要 】

In this paper, we consider a generalized Gardner equation from the point of view of classical and nonclassical symmetries in partial differential equations. We perform a complete analysis of the symmetry reductions by using the similarity variables and the similarity solutions which allow us to reduce our equation into an ordinary differential equation. Moreover, we prove that the nonclassical method applied to the equation leads to new symmetries, which cannot be obtained by using the Lie classical method. Finally, we calculate exact travelling wave solutions of the equation by using the simplest equation method.

【 授权许可】

Unknown