Qawaqneh, H.; Hakami, K.H.; Altalbe, A.; Bayram, M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics2024, 12, 2772.
Qawaqneh, H.; Hakami, K.H.; Altalbe, A.; Bayram, M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics 2024, 12, 2772.
Qawaqneh, H.; Hakami, K.H.; Altalbe, A.; Bayram, M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics2024, 12, 2772.
Qawaqneh, H.; Hakami, K.H.; Altalbe, A.; Bayram, M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics 2024, 12, 2772.
Abstract
This paper is concerned about the novel exact solitons to the truncated M-fractional
(1+1)-dimensional non-linear generalized Bretherton model with arbitrary constants
. This model is used to explain the resonant nonlinear interaction between the waves
in different phenomenon, 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′/G2)-expansion tech-
niques. A novel definition of Fractional derivative provides the solutions distinct from
the present solutions. Mathematica software is used to obtain, and verify the solutions.
The solutions are shown through 2-D, 3-D, and density plots. The stability process
is performed to verify that the solutions are exact and accurate. The modulation
instability is used to determine the steady-state stable results to the corresponding
equation.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
