Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Okara, Okara, Pakistan.

2 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

3 Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.

4 Department of Mathematics, Faculty of Basic Education, University of Kufa, Najaf, Iraq.

5 Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.

Abstract

Optical solitons are self-trapped light beams that maintain their shape and transverse dimension during propagation. This paper investigates the propagation of solitons in an optical material with a weak nonlocal media, modeled by a cubic-quintic-septimal nonlinearity. The dynamics of solitons in optical waveguides are described by the cubic nonlinear Schrödinger equation and its extensions. This equation model applies to both the spatial propagation of beams and the temporal propagation of pulses in a medium exhibiting cubic nonlinearity. The novelty of the paper lies in the application of the extended hyperbolic function method to derive soliton solutions in optical materials with weak nonlocal media in the form of the periodic, bright, kink, and singular type solitons. The obtained solutions provide explicit expressions for the behavior of optical waves in media. These results shed light on the dynamics of nonlinear waves in optical materials and contribute to a better understanding of soliton propagation. The findings contribute to a more comprehensive understanding of the role of nonlocal nonlinearity and time constants in soliton solutions. Our findings provide a better understanding of the dynamics of the nonlinear waves in optical media and have many application for the field of optical communication and signal processing. The role of nonlocal nonlinearity and time constant on soliton solutions is also discussed with the help of graphs.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 1
January 2025
Pages 271-281

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History

  • Receive Date: 01 July 2023
  • Revise Date: 26 February 2024
  • Accept Date: 27 March 2024

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