### Abstract

A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

Original language | English |
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Pages (from-to) | 1191-1206 |

Number of pages | 16 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 5 |

DOIs | |

Publication status | Published - 3 Feb 2006 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

**Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential.** / Litvinets, F. N.; Shapovalov, Aleksandr Vasilievich; Trifonov, A. Yu.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 39, no. 5, pp. 1191-1206. https://doi.org/10.1088/0305-4470/39/5/012

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TY - JOUR

T1 - Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

AU - Litvinets, F. N.

AU - Shapovalov, Aleksandr Vasilievich

AU - Trifonov, A. Yu

PY - 2006/2/3

Y1 - 2006/2/3

N2 - A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

AB - A countable set of asymptotic space-localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross-Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T ≫ 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schrödinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.

UR - http://www.scopus.com/inward/record.url?scp=31144445029&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=31144445029&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/39/5/012

DO - 10.1088/0305-4470/39/5/012

M3 - Article

VL - 39

SP - 1191

EP - 1206

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 5

ER -