Group-invariant Solutions of the 2+1-dimensional Cubic Schr\"odinger Equation
Exactly Solvable and Integrable Systems
2009-11-11 v2
Abstract
Lie point symmetries of the 2+1-dimensional cubic Schr\"odinger 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 Painlev\'e type equations.
Keywords
Cite
@article{arxiv.nlin/0507008,
title = {Group-invariant Solutions of the 2+1-dimensional Cubic Schr\"odinger Equation},
author = {C. Ozemir and F. Gungor},
journal= {arXiv preprint arXiv:nlin/0507008},
year = {2009}
}
Comments
24 pages; typos corrected, new references added