Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law
In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavio...
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4351 |
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| author | Mengke Yu Cailiang Chen Qiuyan Zhang |
| author_facet | Mengke Yu Cailiang Chen Qiuyan Zhang |
| author_sort | Mengke Yu |
| collection | DOAJ |
| description | In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions. |
| first_indexed | 2024-03-10T21:05:17Z |
| format | Article |
| id | doaj.art-ee083f993fa14d22b25cdc26626eb62a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:05:17Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ee083f993fa14d22b25cdc26626eb62a2023-11-19T17:14:48ZengMDPI AGMathematics2227-73902023-10-011120435110.3390/math11204351Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial LawMengke Yu0Cailiang Chen1Qiuyan Zhang2College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, ChinaCollege of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, ChinaCollege of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, ChinaIn this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable traveling-wave system. Then, we discuss the dynamical behavior of the associated regular system and we obtain bifurcations of the phase portraits of the traveling-wave system under different parameter conditions. Finally, under different parameter conditions, we obtain the exact periodic solutions, and the peakon, homoclinic and heteroclinic solutions.https://www.mdpi.com/2227-7390/11/20/4351periodic solutionspeakonhomoclinic orbitheteroclinic orbitthe generalized Radhakrishnan–Kundu–Lakshmanan equation |
| spellingShingle | Mengke Yu Cailiang Chen Qiuyan Zhang Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law Mathematics periodic solutions peakon homoclinic orbit heteroclinic orbit the generalized Radhakrishnan–Kundu–Lakshmanan equation |
| title | Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law |
| title_full | Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law |
| title_fullStr | Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law |
| title_full_unstemmed | Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law |
| title_short | Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law |
| title_sort | bifurcations and exact solutions of the generalized radhakrishnan kundu lakshmanan equation with the polynomial law |
| topic | periodic solutions peakon homoclinic orbit heteroclinic orbit the generalized Radhakrishnan–Kundu–Lakshmanan equation |
| url | https://www.mdpi.com/2227-7390/11/20/4351 |
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