New diverse types of soliton solutions to the Radhakrishnan-Kundu-Lakshmanan equation

Emad H. M. Zahran; Omar Abu Arqub; Ahmet Bekir; Marwan Abukhaled; Emad H. M. Zahran; Omar Abu Arqub; Ahmet Bekir; Marwan Abukhaled

doi:10.3934/math.2023450

AIMS Mathematics

2023, Volume 8, Issue 4: 8985-9008. doi: 10.3934/math.2023450

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New diverse types of soliton solutions to the Radhakrishnan-Kundu-Lakshmanan equation

1.
Department of Mathematical and Physical Engineering, Benha University, Faculty of Engineering, Shubra, Egypt
2.
Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Jordan
3.
Neighbourhood of Akcaglan, Imarli Street, 28/4, 26030, Eskisehir, Turkey
4.
Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates

Received: 28 October 2022 Revised: 11 January 2023 Accepted: 18 January 2023 Published: 10 February 2023
MSC : 35C07, 35Q51, 83C15

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic and were not realized before by any other method. These new forms have been detected by using four different techniques, which are, the extended simple equation method, the Paul-Painlevé approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method. These new solitons will be arranged to create a soliton catalog with new impressive behaviors and they will contribute to future studies not only for this model but also for the optical propagations through birefringent fiber.
Citation: Emad H. M. Zahran, Omar Abu Arqub, Ahmet Bekir, Marwan Abukhaled. New diverse types of soliton solutions to the Radhakrishnan-Kundu-Lakshmanan equation[J]. AIMS Mathematics, 2023, 8(4): 8985-9008. doi: 10.3934/math.2023450

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Abstract

The main purpose of this study was to produce abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation that represents unstable optical solitons that emerge from optical propagations through the use of birefringent fibers. These new types of soliton solutions have behaviors that are bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic and were not realized before by any other method. These new forms have been detected by using four different techniques, which are, the extended simple equation method, the Paul-Painlevé approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method. These new solitons will be arranged to create a soliton catalog with new impressive behaviors and they will contribute to future studies not only for this model but also for the optical propagations through birefringent fiber.

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