Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

Abstract

We study the internal stabilization of the higher order nonlinear Schrodinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrodinger equation with a damping term decays exponentially.