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

*(English)*Zbl 1197.81121Summary: 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 $m\to 1$ and trigonometric function solutions as $m\to 0$, respectively.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.