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This article is cited in 10 scientific papers (total in 10 papers)
Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation
Aleksandr L. Lisoka, Aleksandr V. Shapovalovab, Andrey Yu. Trifonovab a Mathematical Physics Department, Tomsk Polytechnic University,
30 Lenin Ave., Tomsk, 634034 Russia
b Theoretical Physics Department, Tomsk State University,
36 Lenin Ave., Tomsk, 634050 Russia
Abstract:
We consider the symmetry properties of an integro-differential multidimensional Gross–Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross–Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross–Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross–Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained.
Keywords:
symmetry operators; intertwining operators; nonlocal Gross–Pitaevskii equation; semiclassical
asymptotics; exact solutions.
Received: February 15, 2013; in final form October 26, 2013; Published online November 6, 2013
Citation:
Aleksandr L. Lisok, Aleksandr V. Shapovalov, Andrey Yu. Trifonov, “Symmetry and Intertwining Operators for the Nonlocal Gross–Pitaevskii Equation”, SIGMA, 9 (2013), 066, 21 pp.
Linking options:
https://www.mathnet.ru/eng/sigma849 https://www.mathnet.ru/eng/sigma/v9/p66
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