Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential

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dc.creatorShapovalov, Alexander
dc.creatorTrifonov, Andrey
dc.creatorLisok, Alexander
dc.date2005-11-03
dc.date.accessioned2026-07-07T09:34:21Z
dc.date.available2026-07-07T09:34:21Z
dc.descriptionThe 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.
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/0511010
dc.identifierhttp://arxiv.org/abs/math-ph/0511010
dc.identifierSIGMA 1 (2005), 007, 14 pages
dc.identifierdoi:10.3842/SIGMA.2005.007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159463
dc.subjectMathematical Physics
dc.subjectSoft Condensed Matter
dc.subjectExactly Solvable and Integrable Systems
dc.titleExact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential
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