Dynamics and soliton solutions of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity in dispersive media

Tianyong Han; Ying Liang; Wenjie Fan; Tianyong Han; Ying Liang; Wenjie Fan

doi:10.3934/math.2025035

AIMS Mathematics

2025, Volume 10, Issue 1: 754-776. doi: 10.3934/math.2025035

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Dynamics and soliton solutions of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity in dispersive media

1.
College of Computer Science, Chengdu University, Chengdu, 610106, China
2.
Key Laboratory of Digital Innovation of Tianfu Culture, Sichuan Provincial Department of Culture and Tourism, Chengdu University, Chengdu, 610106, China
3.
College of Electronic and Information Engineering, Chengdu Aeronautic Polytechnic, Chengdu, 610100, China
4.
Dazhou Key Laboratory of Multidimensional Data Perception and Intelligent Information Processing, Sichuan Univeristy of Arts and Scinece, Dazhou, 635002, China

Received: 04 November 2024 Revised: 27 December 2024 Accepted: 03 January 2025 Published: 13 January 2025
MSC : 35C08, 35C15, 32W50

This study systematically investigates the dynamics of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity under spatiotemporal dispersion, providing insights into soliton propagation in dispersive media. We begin by examining the system's phase portrait and chaotic behavior, followed by the derivation of exact traveling wave solutions, including optical solitons and periodic solutions, using an enhanced algebraic method. The findings are vividly illustrated through three-dimensional and two-dimensional graphical simulations, which analyze the impact of key parameters on the solutions. This study not only presents a variety of optical soliton solutions, but also clarifies the underlying dynamics, offering theoretical guidance for fiber optic communication systems and holding significant applied value for achieving more efficient and reliable optical communications.
- bifurcation analysis,
- chaos behavior,
- optical soliton,
- perturbed Schrödinger-Hirota equation,
- spatiotemporal dispersion
Citation: Tianyong Han, Ying Liang, Wenjie Fan. Dynamics and soliton solutions of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity in dispersive media[J]. AIMS Mathematics, 2025, 10(1): 754-776. doi: 10.3934/math.2025035

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Abstract

This study systematically investigates the dynamics of the perturbed Schrödinger-Hirota equation with cubic-quintic-septic nonlinearity under spatiotemporal dispersion, providing insights into soliton propagation in dispersive media. We begin by examining the system's phase portrait and chaotic behavior, followed by the derivation of exact traveling wave solutions, including optical solitons and periodic solutions, using an enhanced algebraic method. The findings are vividly illustrated through three-dimensional and two-dimensional graphical simulations, which analyze the impact of key parameters on the solutions. This study not only presents a variety of optical soliton solutions, but also clarifies the underlying dynamics, offering theoretical guidance for fiber optic communication systems and holding significant applied value for achieving more efficient and reliable optical communications.

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