Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 1

Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 1

Bibliographische Detailangaben
Parent link:Symmetry, Integrability and Geometry: Methods and Applications (SIGMA): Scientific Journal
Vol. 1.— 2005.— [14 p.]
1. Verfasser: Shapovalov A. V. Aleksandr Vasilyevich
Weitere Verfasser: Trifonov A. Yu. Andrey Yurievich, Lisok A. L. Aleksandr Leonidovich
Zusammenfassung:Title screen
The complex WKB–Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross–Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors. Although the WKB–Maslov method is approximate in essence, it leads to exact solution of the Gross–Pitaevskii equation with an external and a nonlocal quadratic potential. For this equation, an exact solution of the Cauchy problem is constructed in the class of trajectory concentrated functions. A nonlinear evolution operator is found in explicit form and symmetry operators (mapping a solution of the equation into another solution) are obtained for the equation under consideration. General constructions are illustrated by examples
Sprache:Englisch
Veröffentlicht: 2005
Schlagworte:
электронный ресурс
труды учёных ТПУ
WKB–Maslov complex germ method
semiclassical asymptotics
Gross–Pitaevskii equation
solitons
symmetry operators
Online-Zugang:http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sigma&paperid=7&option_lang=rus
Format: Elektronisch Buchkapitel
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636514

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