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Jacobi elliptic function solutions of the Ablowitz-Ladik discrete nonlinear Schrödinger system. (English) Zbl 1197.81121

Summary: 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 m1 and trigonometric function solutions as m0, 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.

MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
35J99Elliptic equations and systems
35Q55NLS-like (nonlinear Schrödinger) equations