Nonlinear stage of modulation instability

We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing nonlinear Schrödinger equation (NLSE). We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We separate a special designate...

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Bibliographic Details
Published inPhysical review letters Vol. 111; no. 5; p. 054101
Main Authors Zakharov, V E, Gelash, A A
Format Journal Article
LanguageEnglish
Published United States 02.08.2013
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Summary:We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing nonlinear Schrödinger equation (NLSE). We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We separate a special designated class of "regular solitonic solutions" that do not disturb phases of the condensate at infinity by coordinate. All regular solitonic solutions can be treated as localized perturbations of the condensate. We find an important class of "superregular solitonic solutions" which are small perturbations at a certain moment of time. They describe the nonlinear stage of the modulation instability of the condensate.
ISSN:1079-7114
DOI:10.1103/PhysRevLett.111.054101