Abstract
In this article, the generalized multiple Riccati equations rational expansion method has been used to construct a series of complexiton soliton solutions for the non-linear Hirota-Satsuma equations. With the help of symbolic computation software as Maple or Mathematica, we obtain many new types of complexiton soliton solutions, i.e. various combination of trigonometric periodic function and hyperbolic function solutions, various combination of trigonometric periodic function and rational function solutions, and various combination of hyperbolic function and rational function solutions.