Exact solutions and dynamic properties of Ito-Type coupled nonlinear wave equations

Abstract

In this paper, we conduct qualitative and quantitative analysis to Ito system by the complete discrimination system for polynomial method (CDSPM). Through the traveling wave transformation, the original equations could be transformed into a dynamic system. A conserved quantity, namely the Hamiltonian, is established, and then the qualitative properties such as equilibrium points are gotten. Especially, a typical phase portrait is emphasized to present prior estimate of existences of smooth soliton, cusped soliton and periodic solutions. Concrete examples of these solutions are all constructed to verify our conclusion directly.