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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)734-743
Number of pages10
JournalRussian Physics Journal
Volume49
Issue number7
DOIs
Publication statusPublished - 1 Jul 2006

Fingerprint

polar coordinates
strokes
nonlinear equations
approximation
solitary waves
curves

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

@article{66cce17f797c4798afd837714869c164,
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 = "7",
day = "1",
doi = "10.1007/s11182-006-0169-7",
language = "English",
volume = "49",
pages = "734--743",
journal = "Russian Physics Journal",
issn = "1064-8887",
publisher = "Consultants Bureau",
number = "7",

}

TY - JOUR

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.

UR - http://www.scopus.com/inward/record.url?scp=33845484823&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845484823&partnerID=8YFLogxK

U2 - 10.1007/s11182-006-0169-7

DO - 10.1007/s11182-006-0169-7

M3 - Article

AN - SCOPUS:33845484823

VL - 49

SP - 734

EP - 743

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 7

ER -