Kink-type solutions of the SIdV equation and their properties-Reference-Cited by-同舟云学术

Kink-type solutions of the SIdV equation and their properties

Published:2019-08 Issue:8 Volume:6 Page:191040
ISSN:2054-5703
Container-title:Royal Society Open Science
language:en
Short-container-title:R. Soc. open sci.

Author:

Zhang Guofei¹^ORCID,He Jingsong²^ORCID,Wang Lihong¹,Mihalache Dumitru³

Affiliation:

1. School of Mathematics and Statistics, Ningbo University, Zhejiang 315211, People’s Republic of China

2. Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, People’s Republic of China

3. Horia Hulubei National Institute for Physics and Nuclear Engineering, PO Box MG-6, Magurele 077125, Romania

Abstract

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.

Publisher

The Royal Society

Subject

Multidisciplinary

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.191040

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