Symmetry classification of variable coefficient cubic-quintic nonlinear Schr\"{o}dinger equations
Exactly Solvable and Integrable Systems
2015-06-03 v1 Mathematical Physics
math.MP
Abstract
A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schr\"odinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that their symmetry group can be at most four-dimensional in the genuine cubic-quintic nonlinearity. It is only five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equations are of cubic type, and six-dimensional (isomorphic to the Schr\"odinger algebra sch(1)) when they are of quintic type.
Cite
@article{arxiv.1201.4033,
title = {Symmetry classification of variable coefficient cubic-quintic nonlinear Schr\"{o}dinger equations},
author = {C. Özemir and F. Güngör},
journal= {arXiv preprint arXiv:1201.4033},
year = {2015}
}