Semiclassical Spectral Series Localized on a Curve for the Gross–Pitaevskii Equation with a Nonlocal Interaction
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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.
- Tomsk State Pedagogical University Russian Federation
- V.E. Zuev Institute of Atmospheric Optics Russian Federation
- Siberian Branch of the Russian Academy of Sciences Russian Federation
- National Research University of Electronic Technology Russian Federation
- Omsk State University Russian Federation
операторы симметрии, Bose–Einstein condensate, symmetry operators, stationary Gross–Pitaevskii equation, semiclassical approximation, квазиклассическое приближение, nonlocal interaction, nonlinear spectral problem, нелинейная спектральная задача, Гросса-Питаевского уравнение, нелокальное взаимодействие, Бозе-Эйнштейна конденсат
операторы симметрии, Bose–Einstein condensate, symmetry operators, stationary Gross–Pitaevskii equation, semiclassical approximation, квазиклассическое приближение, nonlocal interaction, nonlinear spectral problem, нелинейная спектральная задача, Гросса-Питаевского уравнение, нелокальное взаимодействие, Бозе-Эйнштейна конденсат
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