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On localized solutions of discrete nonlinear Schrodinger equation. An exact result | | P. Pacciani
; V. V. Konotop
; G. Perla Menzala
; | | Date: |
19 Apr 2005 | | Journal: | Physica D, 204 (2005) 122-133 | | Subject: | Pattern Formation and Solitons; Analysis of PDEs; Mathematical Physics; Disordered Systems and Neural Networks | nlin.PS cond-mat.dis-nn math-ph math.AP math.MP | | 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. | | Source: | arXiv, nlin.PS/0504039 | | Services: | Forum | Review | PDF | Favorites | |
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