A semiclassical approximation for the nonstationary two-dimensional nonlinear Schrödinger equation with an external field in polar coordinates

Abstract

For the two-dimensional nonlinear Schrödinger equation (NSE) with an external field in polar coordinates, semiclassical solutions asymptotic in small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, have been constructed. The solutions are constructed in the class of functions which are concentrated in a neighborhood of a closed plane curve and have the form of the one-soliton solution of the one-dimensional NSE in the "fast" variable.

Original language	English
Pages (from-to)	734-743
Number of pages	10
Journal	Russian Physics Journal
Volume	49
Issue number	7
DOIs	https://doi.org/10.1007/s11182-006-0169-7
Publication status	Published - 1 Jul 2006

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1007/s11182-006-0169-7

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title = "A semiclassical approximation for the nonstationary two-dimensional nonlinear Schr{\"o}dinger equation with an external field in polar coordinates",

abstract = "For the two-dimensional nonlinear Schr{\"o}dinger equation (NSE) with an external field in polar coordinates, semiclassical solutions asymptotic in small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, have been constructed. The solutions are constructed in the class of functions which are concentrated in a neighborhood of a closed plane curve and have the form of the one-soliton solution of the one-dimensional NSE in the {"}fast{"} variable.",

author = "Borisov, {A. V.} and Trifonov, {A. Yu} and Shapovalov, {Aleksandr Vasilievich}",

year = "2006",

month = jul,

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doi = "10.1007/s11182-006-0169-7",

language = "English",

volume = "49",

pages = "734--743",

journal = "Russian Physics Journal",

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T1 - A semiclassical approximation for the nonstationary two-dimensional nonlinear Schrödinger equation with an external field in polar coordinates

AU - Borisov, A. V.

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2006/7/1

Y1 - 2006/7/1

N2 - For the two-dimensional nonlinear Schrödinger equation (NSE) with an external field in polar coordinates, semiclassical solutions asymptotic in small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, have been constructed. The solutions are constructed in the class of functions which are concentrated in a neighborhood of a closed plane curve and have the form of the one-soliton solution of the one-dimensional NSE in the "fast" variable.

AB - For the two-dimensional nonlinear Schrödinger equation (NSE) with an external field in polar coordinates, semiclassical solutions asymptotic in small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, have been constructed. The solutions are constructed in the class of functions which are concentrated in a neighborhood of a closed plane curve and have the form of the one-soliton solution of the one-dimensional NSE in the "fast" variable.

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