On preliminary symmetry classification of nonlinear Schrödinger equations with some applications to Doebner-Goldin model

We perform classification of a class of one-dimensional nonlinear Schrodinger equations whose symmetry groups have dimensions n = 1; 2; 3. Next, we select from so constructed classes of invariant equations those nonlinear Schrodinger equations that are invariant with respect to the Galilei group and its natural extensions. The results obtained are applied for symmetry classification of complex Galilei-invariant Doebner-Goldin models.