On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities
The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain th...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/6649285 |
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| author | Nattakorn Sukantamala Supawan Nanta |
| author_facet | Nattakorn Sukantamala Supawan Nanta |
| author_sort | Nattakorn Sukantamala |
| collection | DOAJ |
| description | The nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions. |
| format | Article |
| id | doaj-art-7bbddd228919409ca2e4aa5275c715a9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7bbddd228919409ca2e4aa5275c715a92025-02-03T06:12:31ZengWileyAbstract and Applied Analysis1085-33751687-04092021-01-01202110.1155/2021/66492856649285On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law NonlinearitiesNattakorn Sukantamala0Supawan Nanta1Chiang Mai University, Chiang Mai 50200, ThailandPhetchabun Rajabhat University, Phetchabun 67000, ThailandThe nonlinear wave equation is a significant concern to describe wave behavior and structures. Various mathematical models related to the wave phenomenon have been introduced and extensively being studied due to the complexity of wave behaviors. In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the classical Camassa-Holm equation and the Rosenau-RLW-Kawahara equation with the dual term of nonlinearities is proposed. The solution properties are analytically derived. The new model still satisfies the fundamental energy conservative property as the original models. We then apply the energy method to prove the well-posedness of the model under the solitary wave hypothesis. Some categories of exact solitary wave solutions of the model are described by using the Ansatz method. In addition, we found that the dual term of nonlinearity is essential to obtain the class of analytic solution. Besides, we provide some graphical representations to illustrate the behavior of the traveling wave solutions.http://dx.doi.org/10.1155/2021/6649285 |
| spellingShingle | Nattakorn Sukantamala Supawan Nanta On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities Abstract and Applied Analysis |
| title | On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities |
| title_full | On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities |
| title_fullStr | On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities |
| title_full_unstemmed | On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities |
| title_short | On Solitary Wave Solutions for the Camassa-Holm and the Rosenau-RLW-Kawahara Equations with the Dual-Power Law Nonlinearities |
| title_sort | on solitary wave solutions for the camassa holm and the rosenau rlw kawahara equations with the dual power law nonlinearities |
| url | http://dx.doi.org/10.1155/2021/6649285 |
| work_keys_str_mv | AT nattakornsukantamala onsolitarywavesolutionsforthecamassaholmandtherosenaurlwkawaharaequationswiththedualpowerlawnonlinearities AT supawannanta onsolitarywavesolutionsforthecamassaholmandtherosenaurlwkawaharaequationswiththedualpowerlawnonlinearities |