Multiple soliton solutions of the Korteweg-de Vries in the frame of the time-dependent variable coefficient

This paper aims to investigate exact multiple soliton solutions for Korteweg-de Vries (KdV) with variable coefficients. Based on the similarity transformation and some hyperbolic function methods, multiple wave kink and wave bell shape solutions of the KdV with time dependent variable coefficient are analyzed. Results of this study show that the shapes of multiple kink-type and bell-type solitons can be effectively controlled by selecting some specific form of self-similar variables