Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system

A new general Jacobi elliptic function expansion algorithm is developed to obtain exact solutions for discrete nonlinear systems. Applying this method, many exact Jabobi elliptic function travelling wave solutions for Ablowitz-Ladik discrete nonlinear Schrödinger system are derived. These doubly periodic solutions may degenerate to hyperbolic function solutions including discrete soliton solutions as the modulus m → 1 and trigonometric function solutions as m → 0, respectively.