On classification of intrinsic localized modes for the discrete nonlinear Schrödinger equation

We consider localized modes (discrete breathers) of the discrete nonlinear Schrödinger equation i(d ψ n /d t)= ψ n+1 + ψ n−1 −2 ψ n + σ| ψ n | 2 ψ n , σ=±1, n∈ Z . We study the diversity of the steady-state solutions of the form ψ n ( t)=e i ωt v n and the intervals of the frequency, ω, of their exi...

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Bibliographic Details
Published in:Physica. D 2004-07, Vol.194 (1), p.127-150
Main Authors: Alfimov, G.L., Brazhnyi, V.A., Konotop, V.V.
Format: Article
Language:English
Subjects:
Bifurcations
Discrete breather
Discrete nonlinear Schrödinger equation
Exact sciences and technology
Intrinsic localized modes
Physics
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Summary:We consider localized modes (discrete breathers) of the discrete nonlinear Schrödinger equation i(d ψ n /d t)= ψ n+1 + ψ n−1 −2 ψ n + σ| ψ n | 2 ψ n , σ=±1, n∈ Z . We study the diversity of the steady-state solutions of the form ψ n ( t)=e i ωt v n and the intervals of the frequency, ω, of their existence. The base for the analysis is provided by the anticontinuous limit ( ω negative and large enough) where all the solutions can be coded by the sequences of three symbols “−”, “0” and “+”. Using dynamical systems approach we show that this coding is valid for ωω ∗ and give the complete table of them for the solutions with codes consisting of less than four symbols.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2004.02.001