Semiclassical solutions of the nonlinear schrödinger equation

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Abstract

A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schrödinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schrödinger equation. The leading term of the asymptotic WKBsolution is constructed for the multidimensional NLSE. Special cases are considered for the standard one-dimensional NLSE and for NLSE in cylindrical coordinates.

Original languageEnglish
Pages (from-to)127-138
Number of pages12
JournalJournal of Nonlinear Mathematical Physics
Volume6
Issue number2
DOIs
Publication statusPublished - 1 Jan 1999

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nonlinear equations
Nonlinear Equations
Cylindrical coordinates
cylindrical coordinates
linear equations
Barycentre
Solitary Waves
External Field
center of mass
Linear equation
solitary waves
Term

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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abstract = "A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr{\"o}dinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schr{\"o}dinger equation. The leading term of the asymptotic WKBsolution is constructed for the multidimensional NLSE. Special cases are considered for the standard one-dimensional NLSE and for NLSE in cylindrical coordinates.",
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AB - A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schrödinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass of such a solution is shown to move along with the bicharacteristics of the basic symbol of the corresponding linear Schrödinger equation. The leading term of the asymptotic WKBsolution is constructed for the multidimensional NLSE. Special cases are considered for the standard one-dimensional NLSE and for NLSE in cylindrical coordinates.

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