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 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.