Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102759
Title: Parametric autoresonant excitation of the nonlinear Schrödinger equation
Authors: Friedland, L.
Shagalov, A. G.
Issue Date: 2016
Publisher: American Physical Society
Citation: Friedland L. Parametric autoresonant excitation of the nonlinear Schrödinger equation / L. Friedland, A. G. Shagalov. — DOI 10.1103/PhysRevE.94.042216 // Physical Review E. — 2016. — Vol. 94. — Iss. 4. — 042216.
Abstract: Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics. © 2016 American Physical Society.
Keywords: SCHRODINGER EQUATION
AUTORESONANT EXCITATION
DINGER EQUATION
NONLINEAR SCHRODINGER
PARAMETRIC EXCITATIONS
SPATIAL HARMONIC
SPATIAL HARMONICS EXPANSION
VARIATIONAL PRINCIPLES
WEAKLY NON-LINEAR
NONLINEAR EQUATIONS
URI: http://hdl.handle.net/10995/102759
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84992699712
PURE ID: 1234195
ISSN: 24700045
DOI: 10.1103/PhysRevE.94.042216
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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