In this research, we find the exact traveling wave solutions involving parameters of the
generalized Hirota–Satsuma couple KdV system according to the modified simple equation method
with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions
are derived from the exact traveling wave solutions. It is shown that the modified simple equation
method provides an effective and a more powerful mathematical tool for solving nonlinear evolution
equations in mathematical physics. Comparison between our results and the well-known results will
be presented