The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity
This study investigates a nonlinear Schrödinger equation that includes Kudryashov’s quintic power-law refractive index along with dual-form nonlocal nonlinearity. Employing dynamical systems theory, we analyze the model through a traveling-wave transformation, reducing it to a singular yet integrabl...
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2025-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/12/1922 |
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| author | Cailiang Chen Mengke Yu Qiuyan Zhang |
| author_facet | Cailiang Chen Mengke Yu Qiuyan Zhang |
| author_sort | Cailiang Chen |
| collection | DOAJ |
| description | This study investigates a nonlinear Schrödinger equation that includes Kudryashov’s quintic power-law refractive index along with dual-form nonlocal nonlinearity. Employing dynamical systems theory, we analyze the model through a traveling-wave transformation, reducing it to a singular yet integrable traveling-wave system. The dynamical behavior of the corresponding regular system is examined, revealing phase trajectories bifurcations under varying parameter conditions. Furthermore, explicit solutions—including periodic, homoclinic, and heteroclinic solutions—are derived for distinct parameter regimes. |
| format | Article |
| id | doaj-art-b14f85f2602e44b29893c45bf7923a37 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-b14f85f2602e44b29893c45bf7923a372025-08-20T03:27:33ZengMDPI AGMathematics2227-73902025-06-011312192210.3390/math13121922The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal NonlinearityCailiang Chen0Mengke Yu1Qiuyan 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, ChinaThis study investigates a nonlinear Schrödinger equation that includes Kudryashov’s quintic power-law refractive index along with dual-form nonlocal nonlinearity. Employing dynamical systems theory, we analyze the model through a traveling-wave transformation, reducing it to a singular yet integrable traveling-wave system. The dynamical behavior of the corresponding regular system is examined, revealing phase trajectories bifurcations under varying parameter conditions. Furthermore, explicit solutions—including periodic, homoclinic, and heteroclinic solutions—are derived for distinct parameter regimes.https://www.mdpi.com/2227-7390/13/12/1922Kudryashov’s quintic power lawrefractive indexnonlinear Schrödinger equationbifurcationperiodic solution |
| spellingShingle | Cailiang Chen Mengke Yu Qiuyan Zhang The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity Mathematics Kudryashov’s quintic power law refractive index nonlinear Schrödinger equation bifurcation periodic solution |
| title | The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity |
| title_full | The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity |
| title_fullStr | The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity |
| title_full_unstemmed | The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity |
| title_short | The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity |
| title_sort | bifurcation and exact solution of the nonlinear schrodinger equation with kudryashov s quintic power law of the refractive index together with the dual form of nonlocal nonlinearity |
| topic | Kudryashov’s quintic power law refractive index nonlinear Schrödinger equation bifurcation periodic solution |
| url | https://www.mdpi.com/2227-7390/13/12/1922 |
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