Semiclassical solutions of the nonlinear schrödinger equation

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 language	English
Pages (from-to)	127-138
Number of pages	12
Journal	Journal of Nonlinear Mathematical Physics
Volume	6
Issue number	2
DOIs	https://doi.org/10.2991/jnmp.1999.6.2.2
Publication status	Published - 1 Jan 1999

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.2991/jnmp.1999.6.2.2

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title = "Semiclassical solutions of the nonlinear schr{\"o}dinger equation",

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.",

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

year = "1999",

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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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