Consistent Riccati Expansion and Solvability

Abstract

A consistent Riccati expansion (CRE) is proposed for solving nonlinear systems with the help of a Riccati equation. A system is defined to be CRE solvable if it has a CRE. Various integrable systems are CRE solvable. Furthermore, it is also revealed that many CRE solvable systems, including the Korteweg de-Vries, Kadomtsev-Patviashvili, nonlinear Schr\"dinger and sine-Gordon equations, possess a common determining equation which describes interactions between a soliton and a cnoidal wave.