Soliton solution of the generalized fifth order Hirota-Satsuma equation coupled with KdV

Abstract

We introduced a fifth-order partial differential equation as a generalization of Hirota-Satsuma coupled with KdV system. This equation is investigated based on tanh method. By applying the suitable independent variable in Hirota-Satsuma equation, we can convert this partial differential equations(PDE) into ordinary differential equations(ODE) .Solving the converted Hirota-Satsuma equation by numerical methods we showed this equation have had soliton solution.