Symmetry operators of the two-component Gross - Pitaevskii equation with a Manakov-type nonlocal nonlinearity

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We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated.

Original languageEnglish
Article number012046
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 25 Jan 2016


ASJC Scopus subject areas

  • Physics and Astronomy(all)

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