The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms
In this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthe...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4209275 |
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| author | Wei-Guo Zhang Xing-Qian Ling Xiang Li Shao-Wei Li |
| author_facet | Wei-Guo Zhang Xing-Qian Ling Xiang Li Shao-Wei Li |
| author_sort | Wei-Guo Zhang |
| collection | DOAJ |
| description | In this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthermore, on the basis of the two bell-shaped solitary wave solutions of the equation, the explicit expressions of the orbital stability discriminants are deduced to give the orbitally stable and instable intervals for the two solitary waves as the wave velocity changing. Moreover, the influence caused by the interaction between two nonlinear terms is also discussed. From the conclusion, it can be seen that the influences caused by this interaction are apparently when 0<p<4, which shows the complexity of this system with two nonlinear terms. Finally, by deriving the orbital stability discriminant d′′(c) in the form of Gaussian hypergeometric function, the numerical simulations of several main conclusions are given in this paper. |
| format | Article |
| id | doaj-art-abcfe06ed89e459b81388ffbf74cfad6 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-abcfe06ed89e459b81388ffbf74cfad62025-02-03T01:23:02ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/42092754209275The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear TermsWei-Guo Zhang0Xing-Qian Ling1Xiang Li2Shao-Wei Li3College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaBusiness School, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Mathematics and Information Engineering, Taizhou University, Taizhou 317000, ChinaIn this paper, the orbital stability of solitary wave solutions for the generalized Gardner equation is investigated. Firstly, according to the theory of orbital stability of Grillakis-Shatah-Strauss, a general conclusion is given to determine the orbital stability of solitary wave solutions. Furthermore, on the basis of the two bell-shaped solitary wave solutions of the equation, the explicit expressions of the orbital stability discriminants are deduced to give the orbitally stable and instable intervals for the two solitary waves as the wave velocity changing. Moreover, the influence caused by the interaction between two nonlinear terms is also discussed. From the conclusion, it can be seen that the influences caused by this interaction are apparently when 0<p<4, which shows the complexity of this system with two nonlinear terms. Finally, by deriving the orbital stability discriminant d′′(c) in the form of Gaussian hypergeometric function, the numerical simulations of several main conclusions are given in this paper.http://dx.doi.org/10.1155/2019/4209275 |
| spellingShingle | Wei-Guo Zhang Xing-Qian Ling Xiang Li Shao-Wei Li The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms Complexity |
| title | The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms |
| title_full | The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms |
| title_fullStr | The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms |
| title_full_unstemmed | The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms |
| title_short | The Orbital Stability of Solitary Wave Solutions for the Generalized Gardner Equation and the Influence Caused by the Interactions between Nonlinear Terms |
| title_sort | orbital stability of solitary wave solutions for the generalized gardner equation and the influence caused by the interactions between nonlinear terms |
| url | http://dx.doi.org/10.1155/2019/4209275 |
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