Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation; Arxiv.org

Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation; Arxiv.org

Bibliographic Details
Parent link:	Arxiv.org.— 2013.— Mathematical Physics
Main Author:	Lisok A. L. Aleksandr Leonidovich
Other Authors:	Shapovalov A. V. Aleksandr Vasilyevich, Trifonov A. Yu. Andrey Yurievich
Summary:	Title screen We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained
Language:	English
Published:	2013
Subjects:	электронный ресурс труды учёных ТПУ
Online Access:	http://arxiv.org/abs/1302.3326
Format:	Electronic Book Chapter
KOHA link:	https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636446

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