Construction optical solitons of generalized nonlinear Schrödinger equation with quintuple power-law nonlinearity using Exp-function, projective Riccati, and new generalized methods

Islam Samir; Hamdy M. Ahmed; Wafaa Rabie; W. Abbas; Ola Mostafa; Islam Samir; Hamdy M. Ahmed; Wafaa Rabie; W. Abbas; Ola Mostafa

doi:10.3934/math.2025157

AIMS Mathematics

2025, Volume 10, Issue 2: 3392-3407. doi: 10.3934/math.2025157

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Construction optical solitons of generalized nonlinear Schrödinger equation with quintuple power-law nonlinearity using Exp-function, projective Riccati, and new generalized methods

1.
Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo, Egypt
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
3.
Department of Basic Sciences, Higher Institute of Engineering and Technology, Menoufia, Egypt
4.
Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, Cairo, Egypt

Received: 24 December 2024 Revised: 26 January 2025 Accepted: 12 February 2025 Published: 21 February 2025
MSC : 35C05, 35C07, 35C08, 47J35

This work investigates the generalized nonlinear Schrödinger equation (NLSE), which imitates the wave transmission along optical fibers. This model incorporates a quintuple power-law of non-linearity and nonlinear chromatic dispersion. To demonstrate the significance and motivation for this work, a review of the prior research is presented in the literature. Three integration strategies are applied during the study process in order to produce a variety of novel solutions. These techniques include the modified exp-function approach, the general projective Riccati method (GPRM), and the new generalized method. The extracted solutions include bright solitons, singular solitons, dark solitons, and trigonometric solutions.
- generalized nonlinear Schrödinger equation,
- optical solitons,
- chromatic dispersion,
- analytic methods
Citation: Islam Samir, Hamdy M. Ahmed, Wafaa Rabie, W. Abbas, Ola Mostafa. Construction optical solitons of generalized nonlinear Schrödinger equation with quintuple power-law nonlinearity using Exp-function, projective Riccati, and new generalized methods[J]. AIMS Mathematics, 2025, 10(2): 3392-3407. doi: 10.3934/math.2025157

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Abstract

This work investigates the generalized nonlinear Schrödinger equation (NLSE), which imitates the wave transmission along optical fibers. This model incorporates a quintuple power-law of non-linearity and nonlinear chromatic dispersion. To demonstrate the significance and motivation for this work, a review of the prior research is presented in the literature. Three integration strategies are applied during the study process in order to produce a variety of novel solutions. These techniques include the modified exp-function approach, the general projective Riccati method (GPRM), and the new generalized method. The extracted solutions include bright solitons, singular solitons, dark solitons, and trigonometric solutions.

References

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