Consistent Riccati Expansion and Solvability

2013/08/27 by Sen‐Yue Lou, Lou, S. Y.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1308.5891

openalex publication_date 2013/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrdinger and sine-Gordon equations, possess a common determining equation which describes interactions between a soliton and a cnoidal wave.

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