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.