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

P. Pacciani; V. V. Konotop; G. Perla Menzala

doi:10.1016/j.physd.2005.04.009

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

P. Pacciani·V. V. Konotop·G. Perla Menzala

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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.

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P. Pacciani, V. V. Konotop, G. Perla Menzala. 2005-04-19. On localized solutions of discrete nonlinear Schrodinger equation. An exact result. https://doi.org/10.1016/j.physd.2005.04.009

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