Bifurcations and exact solutions of generalized nonlinear Schrödinger equation
To find the exact explicit solutions of the generalized nonlinear Schrödinger equation, we first give the corresponding differential system for the amplitude component, which constitutes a planar dynamical system featuring a singular straight line. By analyzing its corresponding traveling wave syste...
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025237 |
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| author | Qian Zhang Ai Ke |
| author_facet | Qian Zhang Ai Ke |
| author_sort | Qian Zhang |
| collection | DOAJ |
| description | To find the exact explicit solutions of the generalized nonlinear Schrödinger equation, we first give the corresponding differential system for the amplitude component, which constitutes a planar dynamical system featuring a singular straight line. By analyzing its corresponding traveling wave system, we can derive the dynamical behavior of the amplitude component and give the corresponding phase portraits. Under different parameter conditions, we obtain exact explicit solitary wave solutions, periodic wave solutions, as well as peakons and periodic peakons. By comparing our results with previous studies on the generalized nonlinear Schrödinger equation, we correct the error regarding the first integral and present accurate solutions to the equation. |
| format | Article |
| id | doaj-art-7dafc1ab752d4b759fc93e0ee8a353ad |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7dafc1ab752d4b759fc93e0ee8a353ad2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-03-011035158517210.3934/math.2025237Bifurcations and exact solutions of generalized nonlinear Schrödinger equationQian Zhang0Ai Ke1School of Mathematics and Physics, Southwest University of Science and Technology, Mianyang 621010, Sichuan, ChinaSchool of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, ChinaTo find the exact explicit solutions of the generalized nonlinear Schrödinger equation, we first give the corresponding differential system for the amplitude component, which constitutes a planar dynamical system featuring a singular straight line. By analyzing its corresponding traveling wave system, we can derive the dynamical behavior of the amplitude component and give the corresponding phase portraits. Under different parameter conditions, we obtain exact explicit solitary wave solutions, periodic wave solutions, as well as peakons and periodic peakons. By comparing our results with previous studies on the generalized nonlinear Schrödinger equation, we correct the error regarding the first integral and present accurate solutions to the equation.https://www.aimspress.com/article/doi/10.3934/math.2025237solitary waveperiodic wavepeakonperiodic peakontraveling wave system |
| spellingShingle | Qian Zhang Ai Ke Bifurcations and exact solutions of generalized nonlinear Schrödinger equation AIMS Mathematics solitary wave periodic wave peakon periodic peakon traveling wave system |
| title | Bifurcations and exact solutions of generalized nonlinear Schrödinger equation |
| title_full | Bifurcations and exact solutions of generalized nonlinear Schrödinger equation |
| title_fullStr | Bifurcations and exact solutions of generalized nonlinear Schrödinger equation |
| title_full_unstemmed | Bifurcations and exact solutions of generalized nonlinear Schrödinger equation |
| title_short | Bifurcations and exact solutions of generalized nonlinear Schrödinger equation |
| title_sort | bifurcations and exact solutions of generalized nonlinear schrodinger equation |
| topic | solitary wave periodic wave peakon periodic peakon traveling wave system |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025237 |
| work_keys_str_mv | AT qianzhang bifurcationsandexactsolutionsofgeneralizednonlinearschrodingerequation AT aike bifurcationsandexactsolutionsofgeneralizednonlinearschrodingerequation |