Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations
In this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are tran...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/5303295 |
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| author | Zhao Li Peng Li Tianyong Han |
| author_facet | Zhao Li Peng Li Tianyong Han |
| author_sort | Zhao Li |
| collection | DOAJ |
| description | In this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are transformed into two-dimensional Hamiltonian system by traveling wave transformation and the bifurcation theory. Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. Finally, the stability criteria of the generalized Hirota–Satsuma coupled KdV equations are given. |
| format | Article |
| id | doaj-art-becc939399574b0e8a85096e6f89b64b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-becc939399574b0e8a85096e6f89b64b2025-02-03T05:45:11ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/53032955303295Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV EquationsZhao Li0Peng Li1Tianyong Han2College of Computer Science, Chengdu University, Chengdu 610106, ChinaNorth China Electric Power Test and Research Institute, China Datang Corporation Science and Technology Research Institute Co, Beijing 100040, ChinaCollege of Computer Science, Chengdu University, Chengdu 610106, ChinaIn this paper, the bifurcation, phase portraits, traveling wave solutions, and stability analysis of the fractional generalized Hirota–Satsuma coupled KdV equations are investigated by utilizing the bifurcation theory. Firstly, the fractional generalized Hirota–Satsuma coupled KdV equations are transformed into two-dimensional Hamiltonian system by traveling wave transformation and the bifurcation theory. Then, the traveling wave solutions of the fractional generalized Hirota–Satsuma coupled KdV equations corresponding to phase orbits are easily obtained by applying the method of planar dynamical systems; these solutions include not only the bell solitary wave solutions, kink solitary wave solutions, anti-kink solitary wave solutions, and periodic wave solutions but also Jacobian elliptic function solutions. Finally, the stability criteria of the generalized Hirota–Satsuma coupled KdV equations are given.http://dx.doi.org/10.1155/2021/5303295 |
| spellingShingle | Zhao Li Peng Li Tianyong Han Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations Discrete Dynamics in Nature and Society |
| title | Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations |
| title_full | Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations |
| title_fullStr | Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations |
| title_full_unstemmed | Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations |
| title_short | Bifurcation, Traveling Wave Solutions, and Stability Analysis of the Fractional Generalized Hirota–Satsuma Coupled KdV Equations |
| title_sort | bifurcation traveling wave solutions and stability analysis of the fractional generalized hirota satsuma coupled kdv equations |
| url | http://dx.doi.org/10.1155/2021/5303295 |
| work_keys_str_mv | AT zhaoli bifurcationtravelingwavesolutionsandstabilityanalysisofthefractionalgeneralizedhirotasatsumacoupledkdvequations AT pengli bifurcationtravelingwavesolutionsandstabilityanalysisofthefractionalgeneralizedhirotasatsumacoupledkdvequations AT tianyonghan bifurcationtravelingwavesolutionsandstabilityanalysisofthefractionalgeneralizedhirotasatsumacoupledkdvequations |