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Kink-type solutions of the SIdV equation and their properties.

ABSTRACT: We study the nonlinear integrable equation, u _t + 2((u _x u _xx )/u) = ?u _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.

SUBMITTER: Zhang G

PROVIDER: S-EPMC6731723 | biostudies-literature | 2019 Aug

REPOSITORIES: biostudies-literature

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Kink-type solutions of the SIdV equation and their properties.

Zhang Guofei G He Jingsong J Wang Lihong L Mihalache Dumitru D

Royal Society open science 20190821 8

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 ass ...[more]

PMID: 31598265

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