On localized solutions of discrete nonlinear Schrodinger equation. An exact result
arXiv:nlin/0504039 · doi:10.1016/j.physd.2005.04.009
Abstract
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.
15 pages, accepted for publication in Physica D