The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model

Haitham Qawaqneh, Khalil Hadi Hakami, Ali Altalbe and Mustafa Bayram ()
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Haitham Qawaqneh: Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
Khalil Hadi Hakami: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
Ali Altalbe: Department of Computer Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Mustafa Bayram: Department of Computer and Engineering, Biruni University, Istanbul 34010, Turkey

Mathematics, 2024, vol. 12, issue 17, 1-17

Abstract: This paper is concerned with the novel exact solitons for the truncated M-fractional (1+1)-dimensional nonlinear generalized Bretherton model with arbitrary constants. This model is used to explain the resonant nonlinear interaction between the waves in different phenomena, including fluid dynamics, plasma physics, ocean waves, and many others. A series of exact solitons, including bright, dark, periodic, singular, singular–bright, singular–dark, and other solitons are obtained by applying the extended sinh-Gordon equation expansion (EShGEE) and the modified ( G ′ / G 2 ) -expansion techniques. A novel definition of fractional derivative provides solutions that are distinct from previous solutions. Mathematica software was used to obtain and verify the solutions. The solutions are shown through 2D, 3D, and density plots. A stability process was conducted to verify that the solutions are exact and accurate. Modulation instability was used to determine the steady-state results for the corresponding equation.

Keywords: generalized Bretherton model; fractional derivatives; stability analysis; modulation instability; analytical methods; exact solitons (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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