New single traveling wave solution of the Fokas system via complete discrimination system for polynomial method

Kun Zhang; Tianyong Han; Zhao Li; Kun Zhang; Tianyong Han; Zhao Li

doi:10.3934/math.2023099

AIMS Mathematics

2023, Volume 8, Issue 1: 1925-1936. doi: 10.3934/math.2023099

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Research article

New single traveling wave solution of the Fokas system via complete discrimination system for polynomial method

1.
College of Computer Science, Chengdu University, Chengdu, 610106, China
2.
Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Chengdu University, Chengdu, 610106, China

Received: 13 August 2022 Revised: 10 October 2022 Accepted: 11 October 2022 Published: 26 October 2022
MSC : 35C05, 35C07, 35R11

In this paper, the traveling wave solution of the Fokas system which represents the irregular pulse propagation in monomode optical fibers is studied by using the complete discriminant system method of polynomials. Firstly, the Fokas system is simplified into nonlinear ordinary differential equations by using the traveling wave transformation. Secondly, the Jacobian function solutions, the trigonometric function solutions, the hyperbolic function solutions and the rational function solution of Fokas system are obtained by using the complete discriminant system method of polynomials. Finally, in order to show the propagation of Fokas system in monomode optical fibers, three-dimensional diagram, two-dimensional diagram, contour plot and density plot of some solutions are drawn by using Maple software.
- Fokas system,
- traveling wave solution,
- complete discrimination system
Citation: Kun Zhang, Tianyong Han, Zhao Li. New single traveling wave solution of the Fokas system via complete discrimination system for polynomial method[J]. AIMS Mathematics, 2023, 8(1): 1925-1936. doi: 10.3934/math.2023099

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Abstract

In this paper, the traveling wave solution of the Fokas system which represents the irregular pulse propagation in monomode optical fibers is studied by using the complete discriminant system method of polynomials. Firstly, the Fokas system is simplified into nonlinear ordinary differential equations by using the traveling wave transformation. Secondly, the Jacobian function solutions, the trigonometric function solutions, the hyperbolic function solutions and the rational function solution of Fokas system are obtained by using the complete discriminant system method of polynomials. Finally, in order to show the propagation of Fokas system in monomode optical fibers, three-dimensional diagram, two-dimensional diagram, contour plot and density plot of some solutions are drawn by using Maple software.

References

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