The Gross-Pitaevskii equation with a nonlocal interaction in a semiclassical approximation on a curve A. V. Shapovalov, A. E. Kulagin, A. Yu. Trifonov
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ArticleContent type: Текст Media type: электронный Subject(s): Гросса-Питаевского уравнение | Бозе-Эйнштейна конденсат | операторы симметрии | нелокальное взаимодействие | полуклассическое приближениеGenre/Form: статьи в журналах Online resources: Click here to access online
In:
Symmetry Vol. 12, № 2. P. 201 (1-25)Abstract: 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.
Библиогр.: 56 назв.
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.
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