A study of the symmetry analysis for the Hirota-Satsuma equations

In this work, we present explicit Painleve test for Hirota-Satsuma equation. The invariance and integrability properties of Hirota-Satsuma equation are investigate. Furthermore, using Runge-Kutta-Merson in shooting and matching technique to solve the nonlinear ordinary differential equations which were converted from similarity reduction numerically.