### Abstract

The method of semi-classical asymptotics is applied to a many-dimensional nonlinear Schrodinger equation with an external anisotropic oscillator field. Solutions asymptotic in a small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, are constructed in the class of functions localized in the neighborhood of an unclosed parabolic surface associated with the phase curve that describes the evolution of the vertex of this surface. In the normal direction to the surface, the functions have the form of the one-soliton solution of a one-dimensional nonlinear Schrodinger equation. The asymptotic evolution operator is considered accurate to O(Latin small letter h with stroke ^{3/2}), Latin small letter h with stroke → 0, in the specified class of solutions. The phenomenon of collapse is discussed.

Original language | English |
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Pages (from-to) | 746-753 |

Number of pages | 8 |

Journal | Russian Physics Journal |

Volume | 48 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2005 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**The nonlinear schrodinger equation for a many-dimensional system in an oscillator field.** / Borisov, A. V.; Trifonov, A. Yu; Shapovalov, Aleksandr Vasilievich.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 48, no. 7, pp. 746-753. https://doi.org/10.1007/s11182-005-0196-9

}

TY - JOUR

T1 - The nonlinear schrodinger equation for a many-dimensional system in an oscillator field

AU - Borisov, A. V.

AU - Trifonov, A. Yu

AU - Shapovalov, Aleksandr Vasilievich

PY - 2005/7/1

Y1 - 2005/7/1

N2 - The method of semi-classical asymptotics is applied to a many-dimensional nonlinear Schrodinger equation with an external anisotropic oscillator field. Solutions asymptotic in a small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, are constructed in the class of functions localized in the neighborhood of an unclosed parabolic surface associated with the phase curve that describes the evolution of the vertex of this surface. In the normal direction to the surface, the functions have the form of the one-soliton solution of a one-dimensional nonlinear Schrodinger equation. The asymptotic evolution operator is considered accurate to O(Latin small letter h with stroke 3/2), Latin small letter h with stroke → 0, in the specified class of solutions. The phenomenon of collapse is discussed.

AB - The method of semi-classical asymptotics is applied to a many-dimensional nonlinear Schrodinger equation with an external anisotropic oscillator field. Solutions asymptotic in a small parameter Latin small letter h with stroke, Latin small letter h with stroke → 0, are constructed in the class of functions localized in the neighborhood of an unclosed parabolic surface associated with the phase curve that describes the evolution of the vertex of this surface. In the normal direction to the surface, the functions have the form of the one-soliton solution of a one-dimensional nonlinear Schrodinger equation. The asymptotic evolution operator is considered accurate to O(Latin small letter h with stroke 3/2), Latin small letter h with stroke → 0, in the specified class of solutions. The phenomenon of collapse is discussed.

UR - http://www.scopus.com/inward/record.url?scp=28844486409&partnerID=8YFLogxK

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U2 - 10.1007/s11182-005-0196-9

DO - 10.1007/s11182-005-0196-9

M3 - Article

VL - 48

SP - 746

EP - 753

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 7

ER -