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

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dc.creatorBorisov, Alexey
dc.creatorShapovalov, Alexander
dc.creatorTrifonov, Andrey
dc.date2005-11-27
dc.date.accessioned2026-07-07T09:34:22Z
dc.date.available2026-07-07T09:34:22Z
dc.descriptionThe 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 $\hbar$, $\hbar\to 0$, 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.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0511081
dc.identifierhttp://arxiv.org/abs/math-ph/0511081
dc.identifierSIGMA 1 (2005), 019, 17 pages
dc.identifierdoi:10.3842/SIGMA.2005.019
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159469
dc.subjectMathematical Physics
dc.subjectSoft Condensed Matter
dc.subjectExactly Solvable and Integrable Systems
dc.titleTransverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation
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