Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms
This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since J is not onto, Grillakis-Shatah-Strauss th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/963987 |
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| _version_ | 1832559348568555520 |
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| author | Weiguo Zhang Xu Chen Zhengming Li Haiyan Zhang |
| author_facet | Weiguo Zhang Xu Chen Zhengming Li Haiyan Zhang |
| author_sort | Weiguo Zhang |
| collection | DOAJ |
| description | This paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since J is not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discrimination d′′(c) and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable. |
| format | Article |
| id | doaj-art-59295c2f0a574afdb9023c2bf1cd8673 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-59295c2f0a574afdb9023c2bf1cd86732025-02-03T01:30:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/963987963987Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear TermsWeiguo Zhang0Xu Chen1Zhengming Li2Haiyan Zhang3College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege 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, ChinaThis paper investigates the orbital stability of solitary waves for the generalized symmetric regularized-long-wave equations with two nonlinear terms and analyzes the influence of the interaction between two nonlinear terms on the orbital stability. Since J is not onto, Grillakis-Shatah-Strauss theory cannot be applied on the system directly. We overcome this difficulty and obtain the general conclusion on orbital stability of solitary waves in this paper. Then, according to two exact solitary waves of the equations, we deduce the explicit expression of discrimination d′′(c) and give several sufficient conditions which can be used to judge the orbital stability and instability for the two solitary waves. Furthermore, we analyze the influence of the interaction between two nonlinear terms of the equations on the wave speed interval which makes the solitary waves stable.http://dx.doi.org/10.1155/2014/963987 |
| spellingShingle | Weiguo Zhang Xu Chen Zhengming Li Haiyan Zhang Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms Journal of Applied Mathematics |
| title | Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms |
| title_full | Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms |
| title_fullStr | Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms |
| title_full_unstemmed | Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms |
| title_short | Orbital Stability of Solitary Waves for Generalized Symmetric Regularized-Long-Wave Equations with Two Nonlinear Terms |
| title_sort | orbital stability of solitary waves for generalized symmetric regularized long wave equations with two nonlinear terms |
| url | http://dx.doi.org/10.1155/2014/963987 |
| work_keys_str_mv | AT weiguozhang orbitalstabilityofsolitarywavesforgeneralizedsymmetricregularizedlongwaveequationswithtwononlinearterms AT xuchen orbitalstabilityofsolitarywavesforgeneralizedsymmetricregularizedlongwaveequationswithtwononlinearterms AT zhengmingli orbitalstabilityofsolitarywavesforgeneralizedsymmetricregularizedlongwaveequationswithtwononlinearterms AT haiyanzhang orbitalstabilityofsolitarywavesforgeneralizedsymmetricregularizedlongwaveequationswithtwononlinearterms |