New extended auxiliary equation method for finding many new Jacobi elliptic function solutions of three nonlinear Schrodinger equations

In this paper, we construct many new types of Jacobi elliptic function solutions of nonlinear evolution equations using the so-called new extended auxiliary equation method. The effectiveness of this method is demonstrated by applications to three higher order nonlinear evolution equations, namely, the higher order nonlinear Schrodinger equation with derivative non-Kerr nonlinear terms, the higher order dispersive nonlinear Schrodinger equation and the generalized nonlinear Schrodinger equation. The solitary wave solutions and periodic solutions are obtained from the Jacobi elliptic function solutions. Comparing our new results and the well-known results are given.