Bifurcation analysis and classification of all single traveling wave solution in fiber Bragg gratings with Radhakrishnan-Kundu-Lakshmanan equation

Kun Zhang; Xiaoya He; Zhao Li; Kun Zhang; Xiaoya He; Zhao Li

doi:10.3934/math.2022918

AIMS Mathematics

2022, Volume 7, Issue 9: 16733-16740. doi: 10.3934/math.2022918

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Bifurcation analysis and classification of all single traveling wave solution in fiber Bragg gratings with Radhakrishnan-Kundu-Lakshmanan equation

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, China

Received: 12 May 2022 Revised: 01 July 2022 Accepted: 08 July 2022 Published: 12 July 2022
MSC : 35C05, 35C07, 35R11

The current work studies the bifurcation and the classification of single traveling wave solutions of the coupled version of Radhakrishnan-Kundu-Lakshmanan equation that usually describes the dynamics of optical pulses in fiber Bragg gratings, which is also described by a family of nonlinear Schrödinger equations with cubic nonlinear terms. The solutions of the hyperbolic functions, the rational functions, the trigonometric functions and the Jacobian functions are retrieved by using the complete discrimination system of polynomial. By selecting appropriate parameters, phase portraits, two-dimension graphics and three-dimension graphics of the obtained solutions are drawn.
- Radhakrishnan-Kundu-Lakshmanan,
- single traveling wave solution,
- complete discrimination system,
- bifurcation,
- phase portraits
Citation: Kun Zhang, Xiaoya He, Zhao Li. Bifurcation analysis and classification of all single traveling wave solution in fiber Bragg gratings with Radhakrishnan-Kundu-Lakshmanan equation[J]. AIMS Mathematics, 2022, 7(9): 16733-16740. doi: 10.3934/math.2022918

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Abstract

The current work studies the bifurcation and the classification of single traveling wave solutions of the coupled version of Radhakrishnan-Kundu-Lakshmanan equation that usually describes the dynamics of optical pulses in fiber Bragg gratings, which is also described by a family of nonlinear Schrödinger equations with cubic nonlinear terms. The solutions of the hyperbolic functions, the rational functions, the trigonometric functions and the Jacobian functions are retrieved by using the complete discrimination system of polynomial. By selecting appropriate parameters, phase portraits, two-dimension graphics and three-dimension graphics of the obtained solutions are drawn.

References

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