On localized solutions of discrete nonlinear Schrodinger equation. An exact result
Pacciani, P. · Konotop, V. V. · Menzala, G. Perla
Original · EN
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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