On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions
In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-05-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023031365 |
| _version_ | 1827937485038026752 |
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| author | Baoyong Guo Yong Fang Huanhe Dong |
| author_facet | Baoyong Guo Yong Fang Huanhe Dong |
| author_sort | Baoyong Guo |
| collection | DOAJ |
| description | In this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bilinear forms, the single soliton solutions and the single periodic wave solutions of these two types of equations were obtained respectively. Meanwhile, the figures of the single soliton solutions and the single periodic wave solutions were plotted. Furthermore, the results shed light on that when the amplitude of water wave approaches 0, the single periodic wave solutions tend to the single soliton solutions. The conclusion has been generalized from (2+1)-dimensional equations to (3+1)-dimensional equations. |
| first_indexed | 2024-03-13T08:25:19Z |
| format | Article |
| id | doaj.art-e4ad1223f69e4f93a4c7fc7b1515d5e4 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-03-13T08:25:19Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-e4ad1223f69e4f93a4c7fc7b1515d5e42023-05-31T04:46:01ZengElsevierHeliyon2405-84402023-05-0195e15929On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensionsBaoyong Guo0Yong Fang1Huanhe Dong2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, ChinaCorresponding author.; College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, ChinaIn this paper, the (2+1)-dimensional generalized fifth-order KdV equation and the extended (3+1)-dimensional Jimbo-Miwa equation were transformed into the Hirota bilinear forms with Hirota direct method. In this process, the Hirota bilinear operator played a significant role. Based on the Hirota bilinear forms, the single soliton solutions and the single periodic wave solutions of these two types of equations were obtained respectively. Meanwhile, the figures of the single soliton solutions and the single periodic wave solutions were plotted. Furthermore, the results shed light on that when the amplitude of water wave approaches 0, the single periodic wave solutions tend to the single soliton solutions. The conclusion has been generalized from (2+1)-dimensional equations to (3+1)-dimensional equations.http://www.sciencedirect.com/science/article/pii/S2405844023031365Hirota bilinear operatorSoliton solutionsPeriodic wave solutions(2+1)-dimensional generalized fifth-order KdV equationExtended (3+1)-dimensional Jimbo-Miwa equation |
| spellingShingle | Baoyong Guo Yong Fang Huanhe Dong On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions Heliyon Hirota bilinear operator Soliton solutions Periodic wave solutions (2+1)-dimensional generalized fifth-order KdV equation Extended (3+1)-dimensional Jimbo-Miwa equation |
| title | On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions |
| title_full | On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions |
| title_fullStr | On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions |
| title_full_unstemmed | On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions |
| title_short | On soliton solutions, periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in (2+1) and (3+1) dimensions |
| title_sort | on soliton solutions periodic wave solutions and asymptotic analysis to the nonlinear evolution equations in 2 1 and 3 1 dimensions |
| topic | Hirota bilinear operator Soliton solutions Periodic wave solutions (2+1)-dimensional generalized fifth-order KdV equation Extended (3+1)-dimensional Jimbo-Miwa equation |
| url | http://www.sciencedirect.com/science/article/pii/S2405844023031365 |
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