Single Peak Soliton and Periodic Cusp Wave of the Generalized Schrodinger–Boussinesq Equations*

Abstract

Abstract In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schrödinger–Boussinesq equations. Based on the method of dynamical systems, the generalized Schrödinger–Boussinesq equations are shown to have new the parametric representations of peakon, cuspon, smooth soliton and periodic cusp wave solutions. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.