### 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 |
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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.

Research output: Contribution to journal › Article

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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 -