The Gross–Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve
Copyright policy )The Gross–Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve
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.
- Tomsk Polytechnic University Russian Federation
- Siberian Branch of the Russian Academy of Sciences Russian Federation
- V.E. Zuev Institute of Atmospheric Optics Russian Federation
- National Research University of Electronic Technology Russian Federation
- Tomsk State Pedagogical University Russian Federation
нелокальные взаимодействия, операторы симметрии, Bose–Einstein condensate, complex germ, уравнение Гросса-Питаевского, symmetry operators, бозе-эйнштейновская конденсация, semiclassical approximation, квазиклассическое приближение, nonlocal interaction, полуклассическое приближение, Gross–Pitaevskii equation, Гросса-Питаевского уравнение, нелокальное взаимодействие, Бозе-Эйнштейна конденсат
нелокальные взаимодействия, операторы симметрии, Bose–Einstein condensate, complex germ, уравнение Гросса-Питаевского, symmetry operators, бозе-эйнштейновская конденсация, semiclassical approximation, квазиклассическое приближение, nonlocal interaction, полуклассическое приближение, Gross–Pitaevskii equation, Гросса-Питаевского уравнение, нелокальное взаимодействие, Бозе-Эйнштейна конденсат
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