On the exact solution of (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation

In this paper, symmetry reductions for a cubic nonlinear Schrodinger (NLS) equation to complex ordinary differential equations are presented. These are obtained by means of Lie's method of infinitesimal transformation groups. It is shown that ten types of subgroups of the symmetry group lead, via symmetry reduction, to ordinary differential equations. These equations are solved and the similarity solutions are obtained.