Kink-type solutions of the SIdV equation and their properties

Abstract

We study the nonlinear integrable equation, ut + 2((uxuxx)/u) = ϵuxxx, 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.

Keywords

• darboux transformation
• sidv equation
• korteweg–de vries equation
• kink solution
• decomposition
• phase shift