Kink-type solutions of the SIdV equation and their properties

We study the nonlinear integrable equation, u(t) + 2((u(x)u(xx))/u) = ϵu(xxx), which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen et al. 2012 Commun. Nonlinear Sci. Numer. Simul. 17, 4115–4124 (doi:10.1016/j.cnsns.2012.03.001)). The order-n kink solution...

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Autores principales: Zhang, Guofei, He, Jingsong, Wang, Lihong, Mihalache, Dumitru
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society 2019
Materias:
Mathematics
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6731723/
https://www.ncbi.nlm.nih.gov/pubmed/31598265
http://dx.doi.org/10.1098/rsos.191040
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author Zhang, Guofei
He, Jingsong
Wang, Lihong
Mihalache, Dumitru
author_facet Zhang, Guofei
He, Jingsong
Wang, Lihong
Mihalache, Dumitru
author_sort Zhang, Guofei
collection PubMed
description We study the nonlinear integrable equation, u(t) + 2((u(x)u(xx))/u) = ϵu(xxx), which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen et al. 2012 Commun. Nonlinear Sci. Numer. Simul. 17, 4115–4124 (doi:10.1016/j.cnsns.2012.03.001)). The order-n kink solution u([n]) of the SIdV equation, which is associated with the n-soliton solution of the Korteweg–de Vries equation, is constructed by using the n-fold Darboux transformation (DT) from zero ‘seed’ solution. The kink-type solutions generated by the onefold, twofold and threefold DT are obtained analytically. The key features of these kink-type solutions are studied, namely their trajectories, phase shifts after collision and decomposition into separate single kink solitons.
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spelling pubmed-67317232019-10-09 Kink-type solutions of the SIdV equation and their properties Zhang, Guofei He, Jingsong Wang, Lihong Mihalache, Dumitru R Soc Open Sci Mathematics We study the nonlinear integrable equation, u(t) + 2((u(x)u(xx))/u) = ϵu(xxx), which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen et al. 2012 Commun. Nonlinear Sci. Numer. Simul. 17, 4115–4124 (doi:10.1016/j.cnsns.2012.03.001)). The order-n kink solution u([n]) of the SIdV equation, which is associated with the n-soliton solution of the Korteweg–de Vries equation, is constructed by using the n-fold Darboux transformation (DT) from zero ‘seed’ solution. The kink-type solutions generated by the onefold, twofold and threefold DT are obtained analytically. The key features of these kink-type solutions are studied, namely their trajectories, phase shifts after collision and decomposition into separate single kink solitons. The Royal Society 2019-08-21 /pmc/articles/PMC6731723/ /pubmed/31598265 http://dx.doi.org/10.1098/rsos.191040 Text en © 2019 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Mathematics
Zhang, Guofei
He, Jingsong
Wang, Lihong
Mihalache, Dumitru
Kink-type solutions of the SIdV equation and their properties
title Kink-type solutions of the SIdV equation and their properties
title_full Kink-type solutions of the SIdV equation and their properties
title_fullStr Kink-type solutions of the SIdV equation and their properties
title_full_unstemmed Kink-type solutions of the SIdV equation and their properties
title_short Kink-type solutions of the SIdV equation and their properties
title_sort kink-type solutions of the sidv equation and their properties
topic Mathematics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6731723/
https://www.ncbi.nlm.nih.gov/pubmed/31598265
http://dx.doi.org/10.1098/rsos.191040
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AT hejingsong kinktypesolutionsofthesidvequationandtheirproperties
AT wanglihong kinktypesolutionsofthesidvequationandtheirproperties
AT mihalachedumitru kinktypesolutionsofthesidvequationandtheirproperties

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