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Kink-type solutions of the SIdV equation and their properties
Guofei Zhang1, Jingsong He2, Lihong Wang1
1School of Mathematics and Statistics, Ningbo University, Zhejiang 315211, People's Republic of China.
Abstract:
We study the nonlinear integrable equation, u + 2((u u )/u) = ϵu , 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 [ 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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