Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes

Elsayed M. E. Zayed; Mona El-Shater; Khaled A. E. Alurrfi; Ahmed H. Arnous; Nehad Ali Shah; Jae Dong Chung; Elsayed M. E. Zayed; Mona El-Shater; Khaled A. E. Alurrfi; Ahmed H. Arnous; Nehad Ali Shah; Jae Dong Chung

doi:10.3934/math.2024437

AIMS Mathematics

2024, Volume 9, Issue 4: 8961-8980. doi: 10.3934/math.2024437

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Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes

1.
Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Mathematics, Faculty of Science, Elmergib University, Khoms, Libya
3.
Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El Shorouk Academy, 11837, Cairo, Egypt
4.
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea

Received: 24 November 2023 Revised: 24 January 2024 Accepted: 01 February 2024 Published: 04 March 2024
MSC : 35C08, 35M86, 60H30

This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov's method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions' dynamic behavior and wave structure.
- solitons,
- concatenation model,
- Weierstrass's method,
- addendum to Kudryashov's method,
- new mapping method
Citation: Elsayed M. E. Zayed, Mona El-Shater, Khaled A. E. Alurrfi, Ahmed H. Arnous, Nehad Ali Shah, Jae Dong Chung. Dispersive optical soliton solutions with the concatenation model incorporating quintic order dispersion using three distinct schemes[J]. AIMS Mathematics, 2024, 9(4): 8961-8980. doi: 10.3934/math.2024437

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Abstract

This paper addresses the new concatenation model incorporating quintic-order dispersion, incorporating four well-known nonlinear models. The concatenated models are the nonlinear Schrödinger equation, the Hirota equation, the Lakshmanan-Porsezian-Daniel equation, and the nonlinear Schrödinger equation with quintic-order dispersion. The model itself is innovative and serves as an encouragement for investigating and analyzing the extracted optical solitons. These models play a crucial role in nonlinear optics, especially in studying optical fibers. Three integration algorithms are implemented to investigate the optical solitons with the governing model. These techniques are the Weierstrass-type projective Riccati equation expansion method, the addendum to Kudryashov's method, and the new mapping method. The solutions obtained include various solitons, such as bright, dark, and straddled solitons. Additionally, the paper reports hyperbolic solutions and Weierstrass-type doubly periodic solutions. These solutions are novel and have never been reported before. Visual depictions of some selected solitons illustrate these solutions' dynamic behavior and wave structure.

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