A study of the wave dynamics of the space–time fractional nonlinear evolution equations of beta derivative using the improved Bernoulli sub-equation function approach

The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also modeling s...

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Bibliographic Details
Published in:Scientific reports 2023-11, Vol.13 (1), p.20478-20478, Article 20478
Main Authors: Podder, Anamika, Arefin, Mohammad Asif, Akbar, M. Ali, Uddin, M. Hafiz
Format: Article
Language:English
Subjects:
639/166
639/301/1034
639/705
639/705/1041
Algebra
Applied mathematics
Differential equations
Engineering
Humanities and Social Sciences
multidisciplinary
Ordinary differential equations
Partial differential equations
Physics
Quantum field theory
Science
Science (multidisciplinary)
Shallow water
Software
Tidal waves
Tsunamis
Water waves
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Summary:The space–time fractional nonlinear Klein-Gordon and modified regularized long-wave equations explain the dynamics of spinless ions and relativistic electrons in atom theory, long-wave dynamics in the ocean, like tsunamis and tidal waves, shallow water waves in coastal sea areas, and also modeling several nonlinear optical phenomena. In this study, the improved Bernoulli sub-equation function method has been used to generate some new and more universal closed-form traveling wave solutions of those equations in the sense of beta-derivative. Using the fractional complex wave transformation, the equations are converted into nonlinear differential equations. The achieved outcomes are further inclusive of successfully dealing with the aforementioned models. Some projecting solitons waveforms, including, kink, singular soliton, bell shape, anti-bell shape, and other types of solutions are displayed through a three-dimensional plotline, a plot of contour, and a 2D plot for definite parametric values. It is significant to note that all obtained solutions are verified as accurate by substituting the original equation in each case using the computational software, Maple. Additionally, the results have been compared with other existing results in the literature to show their uniqueness. The proposed technique is effective, computationally attractive, and trustworthy to establish more generalized wave solutions.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-023-45423-6