Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach
We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on d...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/217 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588055405395968 |
|---|---|
| author | Jie Song Feng Li Mingji Zhang |
| author_facet | Jie Song Feng Li Mingji Zhang |
| author_sort | Jie Song |
| collection | DOAJ |
| description | We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family. |
| format | Article |
| id | doaj-art-4dd89b720c32420d8b26c2564a447a19 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4dd89b720c32420d8b26c2564a447a192025-01-24T13:39:46ZengMDPI AGMathematics2227-73902025-01-0113221710.3390/math13020217Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System ApproachJie Song0Feng Li1Mingji Zhang2School of Mathematics and Statistics, Linyi University, Linyi 276005, ChinaSchool of Mathematics and Statistics, Linyi University, Linyi 276005, ChinaDepartment of Mathematics, New Mexico Institution of Mining and Technology, Socorro, NM 87801, USAWe consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family.https://www.mdpi.com/2227-7390/13/2/217solitary waveperiodic wavepseudo-periodic peakonpseudo-peakoncompactonbifurcation |
| spellingShingle | Jie Song Feng Li Mingji Zhang Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach Mathematics solitary wave periodic wave pseudo-periodic peakon pseudo-peakon compacton bifurcation |
| title | Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach |
| title_full | Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach |
| title_fullStr | Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach |
| title_full_unstemmed | Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach |
| title_short | Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach |
| title_sort | bifurcations and exact solutions of the coupled nonlinear generalized zakharov equations with anti cubic nonlinearity dynamical system approach |
| topic | solitary wave periodic wave pseudo-periodic peakon pseudo-peakon compacton bifurcation |
| url | https://www.mdpi.com/2227-7390/13/2/217 |
| work_keys_str_mv | AT jiesong bifurcationsandexactsolutionsofthecouplednonlineargeneralizedzakharovequationswithanticubicnonlinearitydynamicalsystemapproach AT fengli bifurcationsandexactsolutionsofthecouplednonlineargeneralizedzakharovequationswithanticubicnonlinearitydynamicalsystemapproach AT mingjizhang bifurcationsandexactsolutionsofthecouplednonlineargeneralizedzakharovequationswithanticubicnonlinearitydynamicalsystemapproach |