Semiclassical spectral series localized on a curve for the Gross-Pitaevskii equation with a nonlocal interaction

Autor: A. V. Shapovalov, Anton E. Kulagin, Andrey Yu. Trifonov
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Physics and Astronomy (miscellaneous)
General Mathematics
symmetry operators
Semiclassical physics
Space (mathematics)
01 natural sciences
semiclassical approximation
010305 fluids & plasmas
квазиклассическое приближение
nonlocal interaction
nonlinear spectral problem
0103 physical sciences
Computer Science (miscellaneous)
QA1-939
нелинейная спектральная задача
Initial value problem
010306 general physics
нелокальное взаимодействие
Nonlinear Sciences::Pattern Formation and Solitons
Eigenvalues and eigenvectors
Mathematical physics
Physics
Condensed Matter::Quantum Gases
Bose–Einstein condensate
операторы симметрии
Condensed Matter::Other
stationary Gross–Pitaevskii equation
Eigenfunction
Gross–Pitaevskii equation
Chemistry (miscellaneous)
Parametric family
Гросса-Питаевского уравнение
Linear equation
Mathematics
Бозе-Эйнштейна конденсат
Zdroj: Symmetry. 2021. Vol. 132, № 7. P. 1289 (1-22)
Symmetry, Vol 13, Iss 1289, p 1289 (2021)
Symmetry
Volume 13
Issue 7
Popis: 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.
Databáze: OpenAIRE
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