Similarity Wave Excitations for the Generalized Nonautonomous Korteweg-de Vries System

摘要

An exact projective solution to the generalized nonautonomous Korteweg-de Vries system is derived with the aid of a similarity projective approach. All allowed exact solutions of the autonomous KdV equation can be converted into the corresponding exact solutions of the generalized nonautonomous Korteweg-de Vries system. In terms of the known solitary wave solution of the autonomous KdV equation, some novel localized excitations with self-similar behaviors and similaritons are first revealed by prescribing appropriate system parameters.