Symmetry and intertwining operators for the nonlocal gross-pitaevskii equation

Alexander Leonidovich Lisok, Aleksandr Vasilievich Shapovalov, Yu Andrey

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a non local nonlinear (cubic) term in the context of symmetry analysis using the formalism of semi classical asymptotics. This yields a semi classically reduced non local Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semi classical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained.

Original languageEnglish
Article number066
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Publication statusPublished - 6 Nov 2013


  • Exact solutions
  • Intertwining operators
  • Nonlocal gross-pitaevskii equation
  • Semiclassical asymptotics
  • Symmetry operators

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

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