Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients
In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear S...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2021/9955023 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849684030634590208 |
|---|---|
| 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 dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed. |
| format | Article |
| id | doaj-art-c92906fa0b0c4ad8b4f244fa2b64d67b |
| institution | DOAJ |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-c92906fa0b0c4ad8b4f244fa2b64d67b2025-08-20T03:23:35ZengWileyAdvances in Mathematical Physics1687-91201687-91392021-01-01202110.1155/2021/99550239955023Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable CoefficientsZhao 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, ChinaKey Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu 610106, ChinaIn this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.http://dx.doi.org/10.1155/2021/9955023 |
| spellingShingle | Zhao Li Peng Li Tianyong Han Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients Advances in Mathematical Physics |
| title | Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients |
| title_full | Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients |
| title_fullStr | Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients |
| title_full_unstemmed | Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients |
| title_short | Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients |
| title_sort | dynamical behavior and the classification of single traveling wave solutions for the coupled nonlinear schrodinger equations with variable coefficients |
| url | http://dx.doi.org/10.1155/2021/9955023 |
| work_keys_str_mv | AT zhaoli dynamicalbehaviorandtheclassificationofsingletravelingwavesolutionsforthecouplednonlinearschrodingerequationswithvariablecoefficients AT pengli dynamicalbehaviorandtheclassificationofsingletravelingwavesolutionsforthecouplednonlinearschrodingerequationswithvariablecoefficients AT tianyonghan dynamicalbehaviorandtheclassificationofsingletravelingwavesolutionsforthecouplednonlinearschrodingerequationswithvariablecoefficients |