TY  - SER
AU  - Shapovalov,Alexander V.
AU  - Kulagin,Anton E.
AU  - Trifonov,Andrey Yu
TI  - The Gross-Pitaevskii equation with a nonlocal interaction in a semiclassical approximation on a curve
KW  - Гросса-Питаевского уравнение
KW  - Бозе-Эйнштейна конденсат
KW  - операторы симметрии
KW  - нелокальное взаимодействие
KW  - полуклассическое приближение
KW  - статьи в журналах
N1  - Библиогр.: 56 назв
N2  - We propose an approach to constructing semiclassical solutions for the generalized
multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of
 the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over
 time. The approach reduces the Cauchy problem for the nonlocal Gross–Pitaevskii equation to a
 similar problem for the associated linear equation. The geometric properties of the resulting solutions
 are related to Maslov’s complex germ, and the symmetry operators of the associated linear equation
 lead to the approximation of the symmetry operators for the nonlocal Gross–Pitaevskii equation
UR  - http://vital.lib.tsu.ru/vital/access/manager/Repository/vtls:000795006
ER  -