Symmetry classification of variable coefficient cubic-quintic nonlinear Schrodinger equations

A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrodinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that the symmetry group can be at most four-dimensional in the case of genuine cubic-quintic nonlinearity. It may be five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equation is of cubic type, and six-dimensional (isomorphic to the Schrodinger algebra sch(1)) when it is of quintic type. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4789543]