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not-yet-known not-yet-known not-yet-known unknown Optical solitons, qualitative analysis and chaotic behaviors to the highly dispersive nonlinear perturbation Schrödinger equation
  • Yu-Fei Chen
Yu-Fei Chen
Northeast Petroleum University

Corresponding Author:yufei050421@163.com

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Abstract

In this paper, we study the highly dispersive nonlinear perturbation Schrödinger equation, which has arbitrary form of Kudryashov’s with sextic-power law refractive index and generalized non-local laws. For the equation has highly dispersive nonlinear terms and higher order derivatives, it cannot be integrated directly, so we build an integrable factor equation for the approximated equation and apply the trial equation method and the complete discrimination system for polynomial method to create new soliton solutions. On the other hand, we use the bifurcation theory to qualitatively analyze the equation and find the model has periodic solutions, bell-shaped soliton solutions and solitary wave solutions via phase diagrams. The topological stability of the solutions with respect to the parameters is explored in order to better understand the effect of parameters perturbations on the stability of the model’s solutions. Furthermore, we analyze the modulation instability and give the corresponding linear criterion. After accounting for external perturbation terms, we analyze the chaotic behaviors of the equation through the largest Lyapunov exponents and phase diagrams.
Submitted to Mathematical Methods in the Applied Sciences
05 Apr 2024Reviewer(s) Assigned
12 Sep 2024Review(s) Completed, Editorial Evaluation Pending
07 Oct 2024Editorial Decision: Revise Major
12 Oct 20241st Revision Received
14 Oct 2024Submission Checks Completed
14 Oct 2024Assigned to Editor
14 Oct 2024Review(s) Completed, Editorial Evaluation Pending
17 Oct 2024Reviewer(s) Assigned
21 Oct 2024Editorial Decision: Accept