Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

Details Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

2005-09-03

arxiv.org/abs/nlin/0509005v1

Nonlinear Sciences

Pattern Formation and Solitons

12 pages, 2 figures. To appear, Physics Letters A

Scientific paper

10.1016/j.physleta.2005.09.053

We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.

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