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Symmetry 2018, 10(4), 112; https://doi.org/10.3390/sym10040112

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

1
School of Computer Science & Technology, Anhui University of Technology, Ma’anshan 243032, China
2
School of Mathematics & Physics, Anhui University of Technology, Ma’anshan 243032, China
3
College of Mathematics & Systems Science, Shandong University of Science & Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Received: 2 April 2018 / Revised: 11 April 2018 / Accepted: 12 April 2018 / Published: 16 April 2018
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Abstract

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. View Full-Text
Keywords: Gardner equation; compatibility method; symmetry; similarity solution Gardner equation; compatibility method; symmetry; similarity solution
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Zhou, J.; Wang, Y.; Wang, Y.; Yan, Z.; Wang, Z. New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term. Symmetry 2018, 10, 112.

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