Kink-type Solutions of the SIdV Equation and Their Properties

We study the nonlinear integrable equation, + 2(( )/) = , which is invariant under scaling of dependent variable and was called the SIdV equation (see Sen 2012 . , 4115-4124 (doi:10.1016/j.cnsns.2012.03.001)). The order- kink solution of the SIdV equation, which is associated with the -soliton solution of the Korteweg-de Vries equation, is constructed by using the -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.