The Inverse Scattering Transform and Analyticity of Symmetric Solutions for the Integrable Nonlinear Schrödinger Equations

Abstract. We consider the Cauchy problem for an integrable cubic nonlinear Schrödinger equation in one space dimension. We prove global spatial analyticity of solutions via the inverse scattering transform. Consequently we remove the size restriction on the analytic norm when initial data have radially or odd symmetry.