Abstract
We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a non local nonlinear (cubic) term in the context of symmetry analysis using the formalism of semi classical asymptotics. This yields a semi classically reduced non local Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semi classical 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.
| Original language | English |
|---|---|
| Article number | 066 |
| Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| Volume | 9 |
| DOIs | |
| Publication status | Published - 6 Nov 2013 |
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Keywords
- Exact solutions
- Intertwining operators
- Nonlocal gross-pitaevskii equation
- Semiclassical asymptotics
- Symmetry operators
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Mathematical Physics
Cite this
Symmetry and intertwining operators for the nonlocal gross-pitaevskii equation. / Lisok, Alexander Leonidovich; Shapovalov, Aleksandr Vasilievich; Andrey, Yu.
In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 9, 066, 06.11.2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Symmetry and intertwining operators for the nonlocal gross-pitaevskii equation
AU - Lisok, Alexander Leonidovich
AU - Shapovalov, Aleksandr Vasilievich
AU - Andrey, Yu
PY - 2013/11/6
Y1 - 2013/11/6
N2 - We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a non local nonlinear (cubic) term in the context of symmetry analysis using the formalism of semi classical asymptotics. This yields a semi classically reduced non local Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semi classical 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.
AB - We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a non local nonlinear (cubic) term in the context of symmetry analysis using the formalism of semi classical asymptotics. This yields a semi classically reduced non local Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semi classical 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.
KW - Exact solutions
KW - Intertwining operators
KW - Nonlocal gross-pitaevskii equation
KW - Semiclassical asymptotics
KW - Symmetry operators
UR - http://www.scopus.com/inward/record.url?scp=84887179969&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84887179969&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2013.066
DO - 10.3842/SIGMA.2013.066
M3 - Article
AN - SCOPUS:84887179969
VL - 9
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
SN - 1815-0659
M1 - 066
ER -