%0 Journal Article
%T Symmetry classification of variable coefficient cubic-quintic nonlinear Schr£¿dinger equations
%A C. £¿zemir
%A F. G¨¹ng£¿r
%J Physics
%D 2012
%I arXiv
%R 10.1063/1.4789543
%X 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.
%U http://arxiv.org/abs/1201.4033v1