Group-invariant Solutions of the 2+1-dimensional Cubic Schrödinger Equation

Details Group-invariant Solutions of the 2+1-dimensional Cubic Schrödinger Equation Group-invariant Solutions of the 2+1-dimensional Cubic Schrödinger Equation

2005-07-05

arxiv.org/abs/nlin/0507008v2

J. Phys. A: Math. and Gen. V39 (2006) 2973-2993

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages; typos corrected, new references added

Scientific paper

10.1088/0305-4470/39/12/008

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.

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