Lie group method for solving generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) equations

Method of Lie group has been applied to study Hirota–Satsuma coupled Korteweg–de Vries (KdV) system of partial differential equations. Lie group method is applied to determine symmetry reductions of the nonlinear partial differential equations. The resulting nonlinear ordinary differential equations are solved analytically and the obtained solutions are presented graphically.