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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-04-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/4/112 |
| _version_ | 1811263264999342080 |
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| author | Jianping Zhou Yuan Wang Yang Wang Zhilian Yan Zhen Wang |
| author_facet | Jianping Zhou Yuan Wang Yang Wang Zhilian Yan Zhen Wang |
| author_sort | Jianping Zhou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T19:41:35Z |
| format | Article |
| id | doaj.art-091cffac2035470cb8685f12ae950ba3 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:41:35Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-091cffac2035470cb8685f12ae950ba32022-12-22T03:19:03ZengMDPI AGSymmetry2073-89942018-04-0110411210.3390/sym10040112sym10040112New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing TermJianping Zhou0Yuan Wang1Yang Wang2Zhilian Yan3Zhen Wang4School of Computer Science & Technology, Anhui University of Technology, Ma’anshan 243032, ChinaSchool of Computer Science & Technology, Anhui University of Technology, Ma’anshan 243032, ChinaSchool of Computer Science & Technology, Anhui University of Technology, Ma’anshan 243032, ChinaSchool of Mathematics & Physics, Anhui University of Technology, Ma’anshan 243032, ChinaCollege of Mathematics & Systems Science, Shandong University of Science & Technology, Qingdao 266590, ChinaThe 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.http://www.mdpi.com/2073-8994/10/4/112Gardner equationcompatibility methodsymmetrysimilarity solution |
| spellingShingle | Jianping Zhou Yuan Wang Yang Wang Zhilian Yan Zhen Wang New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term Symmetry Gardner equation compatibility method symmetry similarity solution |
| title | New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term |
| title_full | New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term |
| title_fullStr | New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term |
| title_full_unstemmed | New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term |
| title_short | New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term |
| title_sort | new similarity solutions of a generalized variable coefficient gardner equation with forcing term |
| topic | Gardner equation compatibility method symmetry similarity solution |
| url | http://www.mdpi.com/2073-8994/10/4/112 |
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