On certain symmetries of the nonlinear Schrödinger equation

Abstract

In this paper we reduce the problem of symmetries for the Ginzburg-Landau equation to a specific problem of non-classical symmetries for the linear free Schrodinger equation, with the help of an immersion result. This new problem is related to the local U(1)-invariance of the model, and allows us to construct projective representations for arbitrary Lie groups acting on the space-time manifold of the related sigma-model. To achieve this result we propose an enlargement of the usual notion of non-classical symmetry.