Semiclassical Spectral Series Localized on a Curve for the Gross-Pitaevskii Equation with a Nonlocal Interaction

被引：3

作者：

Kulagin, Anton E. ^{[1
,2
]}

Shapovalov, Alexander, V ^{[3
]}

Trifonov, Andrey Y. ^{[1
]}

机构：

[1] Tomsk Polytech Univ, Dept Math & Comp Sci, 30 Lenin A, Tomsk 634050, Russia

[2] Russian Acad Sci, VE Zuev Inst Atmospher Opt, Siberian Branch, 1 Academician Zuev Sq, Tomsk 634055, Russia

[3] Tomsk State Univ, Dept Theoret Phys, 1 Novosobornaya Sq, Tomsk 634050, Russia

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 07期

关键词：

stationary Gross-Pitaevskii equation; nonlocal interaction; nonlinear spectral problem; Bose-Einstein condensate; semiclassical approximation; symmetry operators; BOSE-EINSTEIN CONDENSATION; GROUND-STATE SOLUTION; APPROXIMATION; ASYMPTOTICS; ENERGY;

D O I：

10.3390/sym13071289

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We propose the approach to constructing semiclassical spectral series for the generalized multidimensional stationary Gross-Pitaevskii equation with a nonlocal interaction term. The eigenvalues and eigenfunctions semiclassically concentrated on a curve are obtained. The curve is described by the dynamic system of moments of solutions to the nonlocal Gross-Pitaevskii equation. We solve the eigenvalue problem for the nonlocal stationary Gross-Pitaevskii equation basing on the semiclassical asymptotics found for the Cauchy problem of the parametric family of linear equations associated with the time-dependent Gross-Pitaevskii equation in the space of extended dimension. The approach proposed uses symmetries of equations in the space of extended dimension.

引用

页数：22

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