Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential
Shapovalov, Alexander ; Trifonov, Andrey ; Lisok, Alexander
arXiv, 0511010 / Harvested from arXiv
Text on arXiv
The complex WKB-Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross-Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors. Although the WKB-Maslov method is approximate in essence, it leads to exact solution of the Gross-Pitaevskii equation with an external and a nonlocal quadratic potential. For this equation, an exact solution of the Cauchy problem is constructed in the class of trajectory concentrated functions. A nonlinear evolution operator is found in explicit form and symmetry operators (mapping a solution of the equation into another solution) are obtained for the equation under consideration. General constructions are illustrated by examples.
Publié le : 2005-11-03
Classification:  Mathematical Physics,  Condensed Matter - Soft Condensed Matter,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0511010,
     author = {Shapovalov, Alexander and Trifonov, Andrey and Lisok, Alexander},
     title = {Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii
  Equation with Quadratic Potential},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511010}
}

Shapovalov, Alexander; Trifonov, Andrey; Lisok, Alexander. Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii
  Equation with Quadratic Potential. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511010/