### Abstract

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 language | English |
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Article number | 012046 |

Journal | Journal of Physics: Conference Series |

Volume | 670 |

Issue number | 1 |

DOIs | |

Publication status | Published - 25 Jan 2016 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Symmetry operators of the two-component Gross - Pitaevskii equation with a Manakov-type nonlocal nonlinearity.** / Shapovalov, A. V.; Trifonov, Adrey Yurievich; Lisok, A. L.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Symmetry operators of the two-component Gross - Pitaevskii equation with a Manakov-type nonlocal nonlinearity

AU - Shapovalov, A. V.

AU - Trifonov, Adrey Yurievich

AU - Lisok, A. L.

PY - 2016/1/25

Y1 - 2016/1/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84962360680&partnerID=8YFLogxK

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U2 - 10.1088/1742-6596/670/1/012046

DO - 10.1088/1742-6596/670/1/012046

M3 - Article

VL - 670

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012046

ER -