Abstract
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.
Original language | English |
---|---|
Article number | 007 |
Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
Volume | 1 |
DOIs | |
Publication status | Published - 1 Jan 2005 |
Keywords
- Gross-pitaevskii equation
- Nonlinear evolution operator
- Semiclassical asymptotics
- Symmetry operators
- The cauchy problem
- Trajectory concentrated functions
- Wkb-maslov complex germ method
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Geometry and Topology