Group-invariant Solutions of the 2+1-dimensional Cubic Schrödinger Equation
arXiv:nlin/0507008 · doi:10.1088/0305-4470/39/12/008
Abstract
Lie point symmetries of the 2+1-dimensional cubic Schrödinger equation to obtain new analytic solutions in a systematic manner. We present an analysis of the reduced ODEs, and in particular show that although the original equation is not integrable they typically can belong to the class of Painlevé type equations.
24 pages; typos corrected, new references added