Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions

There is no denying fact that harmonic crystals, cold plasma or liquids and compressible fluids are usually dependent of acoustic-gravity waves, acoustic waves, hydromagnetic waves, surface waves with long wavelength and few others. In this context, the exact solutions of the modified Camassa-Holm e...

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Autores principales:	Yokuş Asıf, Durur Hülya, Abro Kashif Ali
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	(g′ / g − 1 / g)-expansion method (1 / g′)-expansion method modified camassa-holm equation traveling wave solutions comparative analysis Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/6dacbbca5f2b4dfbaeb80cf957bf758f
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spelling	oai:doaj.org-article:6dacbbca5f2b4dfbaeb80cf957bf758f2021-12-05T14:10:57ZRole of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions2192-80102192-802910.1515/nleng-2021-0030https://doaj.org/article/6dacbbca5f2b4dfbaeb80cf957bf758f2021-11-01T00:00:00Zhttps://doi.org/10.1515/nleng-2021-0030https://doaj.org/toc/2192-8010https://doaj.org/toc/2192-8029There is no denying fact that harmonic crystals, cold plasma or liquids and compressible fluids are usually dependent of acoustic-gravity waves, acoustic waves, hydromagnetic waves, surface waves with long wavelength and few others. In this context, the exact solutions of the modified Camassa-Holm equation have been successfully constructed on the basis of comparative analysis of (G′ / G − 1 / G) and (1 / G′)-expansion methods. The (G′ / G − 1 / G) and (1 / G′)-expansion methods have been proved to be powerful and systematic tool for obtaining the analytical solutions of nonlinear partial differential equations so called modified Camassa-Holm equation. The solutions investigated via (G′ / G − 1 / G) and (1 / G′)-expansion methods have remarkably generated trigonometric, hyperbolic, complex hyperbolic and rational traveling wave solutions. For the sake of different traveling wave solutions, we depicted 3-dimensional, 2-dimensional and contour graphs subject to the specific values of the parameters involved in the governing equation. Two methods, which are important instruments in generating traveling wave solutions in mathematics, were compared both qualitatively and quantitatively. In addition, advantages and disadvantages of both methods are discussed and their advantages and disadvantages are revealed.Yokuş AsıfDurur HülyaAbro Kashif AliDe Gruyterarticle(g′ / g − 1 / g)-expansion method(1 / g′)-expansion methodmodified camassa-holm equationtraveling wave solutionscomparative analysisEngineering (General). Civil engineering (General)TA1-2040ENNonlinear Engineering, Vol 10, Iss 1, Pp 385-394 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	(g′ / g − 1 / g)-expansion method (1 / g′)-expansion method modified camassa-holm equation traveling wave solutions comparative analysis Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	(g′ / g − 1 / g)-expansion method (1 / g′)-expansion method modified camassa-holm equation traveling wave solutions comparative analysis Engineering (General). Civil engineering (General) TA1-2040 Yokuş Asıf Durur Hülya Abro Kashif Ali Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
description	There is no denying fact that harmonic crystals, cold plasma or liquids and compressible fluids are usually dependent of acoustic-gravity waves, acoustic waves, hydromagnetic waves, surface waves with long wavelength and few others. In this context, the exact solutions of the modified Camassa-Holm equation have been successfully constructed on the basis of comparative analysis of (G′ / G − 1 / G) and (1 / G′)-expansion methods. The (G′ / G − 1 / G) and (1 / G′)-expansion methods have been proved to be powerful and systematic tool for obtaining the analytical solutions of nonlinear partial differential equations so called modified Camassa-Holm equation. The solutions investigated via (G′ / G − 1 / G) and (1 / G′)-expansion methods have remarkably generated trigonometric, hyperbolic, complex hyperbolic and rational traveling wave solutions. For the sake of different traveling wave solutions, we depicted 3-dimensional, 2-dimensional and contour graphs subject to the specific values of the parameters involved in the governing equation. Two methods, which are important instruments in generating traveling wave solutions in mathematics, were compared both qualitatively and quantitatively. In addition, advantages and disadvantages of both methods are discussed and their advantages and disadvantages are revealed.
format	article
author	Yokuş Asıf Durur Hülya Abro Kashif Ali
author_facet	Yokuş Asıf Durur Hülya Abro Kashif Ali
author_sort	Yokuş Asıf
title	Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
title_short	Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
title_full	Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
title_fullStr	Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
title_full_unstemmed	Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions
title_sort	role of shallow water waves generated by modified camassa-holm equation: a comparative analysis for traveling wave solutions
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/6dacbbca5f2b4dfbaeb80cf957bf758f
work_keys_str_mv	AT yokusasıf roleofshallowwaterwavesgeneratedbymodifiedcamassaholmequationacomparativeanalysisfortravelingwavesolutions AT dururhulya roleofshallowwaterwavesgeneratedbymodifiedcamassaholmequationacomparativeanalysisfortravelingwavesolutions AT abrokashifali roleofshallowwaterwavesgeneratedbymodifiedcamassaholmequationacomparativeanalysisfortravelingwavesolutions
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Role of shallow water waves generated by modified Camassa-Holm equation: A comparative analysis for traveling wave solutions

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