Justification of the coupled mode asymptotics for localized wavepackets in the periodic nonlinear Schrodinger equation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:450

Article

Dohnal, Tomas¹  Helfmeier, Lisa¹ 

[1] Tech Univ Dortmund, Dept Math, D-44221 Dortmund, Germany

关键词: Periodic structure;    Coupled mode equations;    Wavepacket;    Envelope approximation;    Gross-Pitaevskii;    Bloch transformation;   

DOI  :  10.1016/j.jmaa.2017.01.039

来源: Elsevier

【 摘 要 】

We consider wavepackets composed of two modulated carrier Bloch waves with opposite group velocities in the one dimensional periodic Nonlinear Schrlidinger/ Gross Pitaevskii equation. These can be approximated by first order coupled mode equations (CMEs) for the two slowly varying envelopes. Under a suitably selected periodic perturbation of the periodic structure the CMEs possess a spectral gap of the corresponding spatial operator and allow families of exponentially localised solitary waves parametrized by velocity. This leads to a family of approximate solitary waves in the periodic nonlinear Schrodinger equation. Besides a formal derivation of the CMEs a rigorous justification of the approximation and an error estimate in the supremum norm are provided. Several numerical tests corroborate the analysis. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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