Consistent Riccati Expansion and Solvability
Exactly Solvable and Integrable Systems
2013-09-02 v2 Mathematical Physics
math.MP
Pattern Formation and Solitons
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.
Cite
@article{arxiv.1308.5891,
title = {Consistent Riccati Expansion and Solvability},
author = {S. Y. Lou},
journal= {arXiv preprint arXiv:1308.5891},
year = {2013}
}
Comments
15 pages, 0 figures