Solitary Wave Solutions: Method of Invariant Painlevé Analysis and Linearised Riccati System of Equations with Variable Coefficients

A new method to find solitary wave solutions of the nonlinear evolutions is investigated. The method of invariant Painlevé analysis and linearised Riccati system of equations with variable coefficients, abbreviated as APIRTP is a method based on singular manifold analysis. The expressions of the singular manifold are simplified in the form of Schwarzian derivative S. S is a variable coefficient of the Riccati equations. By using the APIRTP method, the truncated solution expansions and solitary wave solutions of the KdV and HKdV equations are obtained.