Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system

The generalized Jacobi elliptic function method is further improved by picking up an elliptic equation's new solutions and introducing a general ansaetz. It is very powerful to uniformly construct more new exact doubly-periodic solutions in terms of rational formal Jacobi elliptic function of nonlinear evolution equations (NLEEs). As an application of the method, we choose the generalized Ito system to illustrate the method. The solitary wave solutions and triangular periodic solutions can be obtained at their limit condition