Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation

Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation

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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