Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation

Details Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation Exact Moving and Stationary Solutions of a Generalized Discrete Nonlinear Schrodinger Equation

2006-12-06

arxiv.org/abs/nlin/0612012v2

Nonlinear Sciences

Pattern Formation and Solitons

22 pages, 7 figures, to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/40/37/008

We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving pulse solution. We also address the problem of finding exact stationary solutions and, for a particular case of the model when stationary solutions can be expressed through the Jacobi elliptic functions, we present a two-point map from which all possible stationary solutions can be found. Numerically we demonstrate the generic stability of the stationary pulse solutions and also the robustness of moving pulses in long-term dynamics.

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