Exact solutions and symmetry operators for the nonlocal Gross-Pitaevskii equation with quadratic potential

Результат исследований: Материалы для журналаСтатья

10 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Номер статьи007
ЖурналSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Том1
DOI
СостояниеОпубликовано - 1 янв 2005

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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