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Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique

Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fiber system, turbulence, nonlinear biological systems, and contr...

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Autores principales: Zaman, U. H. M., Arefin, Mohammad Asif, Akbar, M. Ali, Uddin, M. Hafiz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10202309/
https://www.ncbi.nlm.nih.gov/pubmed/37216390
http://dx.doi.org/10.1371/journal.pone.0285178
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author Zaman, U. H. M.
Arefin, Mohammad Asif
Akbar, M. Ali
Uddin, M. Hafiz
author_facet Zaman, U. H. M.
Arefin, Mohammad Asif
Akbar, M. Ali
Uddin, M. Hafiz
author_sort Zaman, U. H. M.
collection PubMed
description Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fiber system, turbulence, nonlinear biological systems, and control theory. In this research, we chose to construct some new closed form solutions of traveling wave of fractional order nonlinear coupled type Boussinesq–Burger (BB) and coupled type Boussinesq equations. In beachside ocean and coastal engineering, the suggested equations are frequently used to explain the spread of shallow-water waves, depict the propagation of waves through dissipative and nonlinear media, and appears during the investigation of the flow of fluid within a dynamic system. The subsidiary extended tanh-function technique for the suggested equations is solved for achieve new results by conformable derivatives. The fractional order differential transform was used to simplify the solution process by converting fractional differential equations to ordinary type differential equations by using the mentioned method. Using this technique, some applicable wave forms of solitons like bell type, kink type, singular kink, multiple kink, periodic wave, and many other types solution were accomplished, and we express our achieve solutions by 3D, contour, list point, and vector plots by using mathematical software such as MATHEMATICA to express the physical sketch much more clearly. Moreover, we assured that the suggested technique is more reliable, pragmatic, and dependable, that also explore more general exact solutions of close form traveling waves.
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spelling pubmed-102023092023-05-23 Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique Zaman, U. H. M. Arefin, Mohammad Asif Akbar, M. Ali Uddin, M. Hafiz PLoS One Research Article Nonlinear fractional partial differential equations are highly applicable for representing a wide variety of features in engineering and research, such as shallow-water, oceanography, fluid dynamics, acoustics, plasma physics, optical fiber system, turbulence, nonlinear biological systems, and control theory. In this research, we chose to construct some new closed form solutions of traveling wave of fractional order nonlinear coupled type Boussinesq–Burger (BB) and coupled type Boussinesq equations. In beachside ocean and coastal engineering, the suggested equations are frequently used to explain the spread of shallow-water waves, depict the propagation of waves through dissipative and nonlinear media, and appears during the investigation of the flow of fluid within a dynamic system. The subsidiary extended tanh-function technique for the suggested equations is solved for achieve new results by conformable derivatives. The fractional order differential transform was used to simplify the solution process by converting fractional differential equations to ordinary type differential equations by using the mentioned method. Using this technique, some applicable wave forms of solitons like bell type, kink type, singular kink, multiple kink, periodic wave, and many other types solution were accomplished, and we express our achieve solutions by 3D, contour, list point, and vector plots by using mathematical software such as MATHEMATICA to express the physical sketch much more clearly. Moreover, we assured that the suggested technique is more reliable, pragmatic, and dependable, that also explore more general exact solutions of close form traveling waves. Public Library of Science 2023-05-22 /pmc/articles/PMC10202309/ /pubmed/37216390 http://dx.doi.org/10.1371/journal.pone.0285178 Text en © 2023 Zaman et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Zaman, U. H. M.
Arefin, Mohammad Asif
Akbar, M. Ali
Uddin, M. Hafiz
Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title_full Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title_fullStr Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title_full_unstemmed Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title_short Study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
title_sort study of the soliton propagation of the fractional nonlinear type evolution equation through a novel technique
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10202309/
https://www.ncbi.nlm.nih.gov/pubmed/37216390
http://dx.doi.org/10.1371/journal.pone.0285178
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