New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term

The compatibility method is used for a generalized variable-coefficient Gardner equation (GVGE) with a forcing term. By the compatibility of the considered equation and a non-classical symmetry of a given form, four types of symmetry are obtained. Then, by solving the characteristic equations of sym...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 10; no. 4; p. 112
Main Authors Zhou, Jianping, Wang, Yuan, Wang, Yang, Yan, Zhilian, Wang, Zhen
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2018
Subjects
Coefficients
Compatibility
compatibility method
Differential equations
Gardner equation
Mathematical analysis
Nonlinear equations
Nonlinear evolution equations
Ordinary differential equations
Similarity
similarity solution
Similarity solutions
Symmetry
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Summary:The compatibility method is used for a generalized variable-coefficient Gardner equation (GVGE) with a forcing term. By the compatibility of the considered equation and a non-classical symmetry of a given form, four types of symmetry are obtained. Then, by solving the characteristic equations of symmetry, the GVGE is reduced to variable coefficients ordinary differential equations, and rich varieties of new similarity solutions are presented. Our results show that the compatibility method can be employed for variable coefficients nonlinear evolution equations with forcing terms.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym10040112