Abstract
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{stroke}, h{stroke} → 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples.
| Original language | English |
|---|---|
| Article number | 019 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 1 |
| DOIs | |
| Publication status | Published - 2005 |
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Keywords
- Gross-pitaev-skii equation
- Semiclassical asymptotics
- Solitons
- Symmetry operators
- Wkb-maslov complex germ method
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Mathematical Physics
Cite this
Transverse evolution operator for the Gross-Pitaevskii equation in semiclassical approximation. / Borisov, Alexey; Shapovalov, Aleksandr Vasilievich; Trifonov, Andrey.
In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 1, 019, 2005.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Transverse evolution operator for the Gross-Pitaevskii equation in semiclassical approximation
AU - Borisov, Alexey
AU - Shapovalov, Aleksandr Vasilievich
AU - Trifonov, Andrey
PY - 2005
Y1 - 2005
N2 - 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{stroke}, h{stroke} → 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples.
AB - 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{stroke}, h{stroke} → 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples.
KW - Gross-pitaev-skii equation
KW - Semiclassical asymptotics
KW - Solitons
KW - Symmetry operators
KW - Wkb-maslov complex germ method
UR - http://www.scopus.com/inward/record.url?scp=84889234819&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84889234819&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2005.019
DO - 10.3842/SIGMA.2005.019
M3 - Article
VL - 1
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 019
ER -