Properties of real-analytic solutions of the nonlinear Schrödinger equation and related equations

We prove that every local real-analytic solution of the focusing nonlinear Schrödinger equation in dimension 1+1 can be extended analytically to a strip (which can sometimes be enlarged to a half-plane or the whole plane) parallel to the axis of the spatial variable, and this also holds in the defocusing case if we admit singularities of pole type. The question of the maximal domain of analyticity of solutions and the possible types of singularities will be discussed for the vector and matrix versions of NLS as well as for the equations in their hierarchies and, moreover, for the Heisenberg magnetic model and the Landau–Lifshits equation.