Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2005
• Main Authors: Borisov, A., Shapovalov, A., Trifonov, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2005
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209341
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation / A. Borisov, A. Shapovalov, A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 33 назв. — англ.

The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in semiclassical approximation in a small parameter h, h → 0, in...