Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations
In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021641?viewType=HTML |
| _version_ | 1818903083641470976 |
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| author | Wen-Xin Zhang Yaqing Liu |
| author_facet | Wen-Xin Zhang Yaqing Liu |
| author_sort | Wen-Xin Zhang |
| collection | DOAJ |
| description | In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation. |
| first_indexed | 2024-12-19T20:45:54Z |
| format | Article |
| id | doaj.art-21d236b8ab334ae193684c21adf7c5d4 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T20:45:54Z |
| publishDate | 2021-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-21d236b8ab334ae193684c21adf7c5d42022-12-21T20:06:14ZengAIMS PressAIMS Mathematics2473-69882021-07-01610110461107510.3934/math.2021641Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equationsWen-Xin Zhang0Yaqing Liu1School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaSchool of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaIn this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation.https://www.aimspress.com/article/doi/10.3934/math.2021641?viewType=HTMLnonlocal cmkdv equationsoliton solutionshirota bilinear methodintegrabilitylax pair |
| spellingShingle | Wen-Xin Zhang Yaqing Liu Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations AIMS Mathematics nonlocal cmkdv equation soliton solutions hirota bilinear method integrability lax pair |
| title | Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations |
| title_full | Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations |
| title_fullStr | Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations |
| title_full_unstemmed | Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations |
| title_short | Solitary wave solutions and integrability for generalized nonlocal complex modified Korteweg-de Vries (cmKdV) equations |
| title_sort | solitary wave solutions and integrability for generalized nonlocal complex modified korteweg de vries cmkdv equations |
| topic | nonlocal cmkdv equation soliton solutions hirota bilinear method integrability lax pair |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021641?viewType=HTML |
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