Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.

In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahon...

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Autores principales:	S A El-Tantawy, Alvaro H Salas, Castillo H Jairo E
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/ce9f06d2efec40f3bcfb87f3250f7bf3
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spelling	oai:doaj.org-article:ce9f06d2efec40f3bcfb87f3250f7bf32021-12-02T20:14:06ZStability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.1932-620310.1371/journal.pone.0254816https://doaj.org/article/ce9f06d2efec40f3bcfb87f3250f7bf32021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0254816https://doaj.org/toc/1932-6203In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahony (BBM) equation, etc.) are reported in detail using different techniques. The single and periodic peakons are investigated by studying the stability analysis of the gDP equation. The novel compacton solutions to the equations under consideration are derived in the form of Weierstrass elliptic function. Also, the periodicity of these solutions is obtained. The cnoidal wave solutions are obtained in the form of Jacobi elliptic functions. Moreover, both soliton and trigonometric solutions are covered as a special case for the cnoidal wave solutions. Finally, a new form for the peakon solution is derived in details. As an application to this study, the fluid basic equations of a collisionless unmagnetized non-Maxwellian plasma is reduced to the equation under consideration for studying several nonlinear structures in the plasma model.S A El-TantawyAlvaro H SalasCastillo H Jairo EPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 9, p e0254816 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q S A El-Tantawy Alvaro H Salas Castillo H Jairo E Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
description	In this work two kinds of smooth (compactons or cnoidal waves and solitons) and nonsmooth (peakons) solutions to the general Degasperis-Procesi (gDP) equation and its family (Degasperis-Procesi (DP) equation, modified DP equation, Camassa-Holm (CH) equation, modified CH equation, Benjamin-Bona-Mahony (BBM) equation, etc.) are reported in detail using different techniques. The single and periodic peakons are investigated by studying the stability analysis of the gDP equation. The novel compacton solutions to the equations under consideration are derived in the form of Weierstrass elliptic function. Also, the periodicity of these solutions is obtained. The cnoidal wave solutions are obtained in the form of Jacobi elliptic functions. Moreover, both soliton and trigonometric solutions are covered as a special case for the cnoidal wave solutions. Finally, a new form for the peakon solution is derived in details. As an application to this study, the fluid basic equations of a collisionless unmagnetized non-Maxwellian plasma is reduced to the equation under consideration for studying several nonlinear structures in the plasma model.
format	article
author	S A El-Tantawy Alvaro H Salas Castillo H Jairo E
author_facet	S A El-Tantawy Alvaro H Salas Castillo H Jairo E
author_sort	S A El-Tantawy
title	Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
title_short	Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
title_full	Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
title_fullStr	Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
title_full_unstemmed	Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.
title_sort	stability analysis and novel solutions to the generalized degasperis procesi equation: an application to plasma physics.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/ce9f06d2efec40f3bcfb87f3250f7bf3
work_keys_str_mv	AT saeltantawy stabilityanalysisandnovelsolutionstothegeneralizeddegasperisprocesiequationanapplicationtoplasmaphysics AT alvarohsalas stabilityanalysisandnovelsolutionstothegeneralizeddegasperisprocesiequationanapplicationtoplasmaphysics AT castillohjairoe stabilityanalysisandnovelsolutionstothegeneralizeddegasperisprocesiequationanapplicationtoplasmaphysics
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Stability analysis and novel solutions to the generalized Degasperis Procesi equation: An application to plasma physics.

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