On localized solutions of discrete nonlinear Schrodinger equation. An exact result

Details On localized solutions of discrete nonlinear Schrodinger equation. An exact result On localized solutions of discrete nonlinear Schrodinger equation. An exact result

2005-04-19

arxiv.org/abs/nlin/0504039v1

Physica D, 204 (2005) 122-133

Nonlinear Sciences

Pattern Formation and Solitons

15 pages, accepted for publication in Physica D

Scientific paper

10.1016/j.physd.2005.04.009

Local and global existence of localized solutions of a discrete nonlinear Schrodinger (DNLS) equation, with arbitrary on-site nonlinearity, is proved. In particular, it is shown that an initially localized excitation persists localized during infinite time. Moreover, if initial localization is stronger than |n|^{-d} with any power d, it maintains itself as such during infinite time. The results are generalized to various types of inter-side and saturable nonlinearities, to lattices with long range interactions, as well as DNLS with dissipation.

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