Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d

Abstract

Abstract. We consider the one dimensional nonlinear Schrö dinger equation iu t þ u xx =2 ¼ f ðuÞ, x A R, t > 0, uð0; xÞ ¼ u 0 ðxÞ, x A R, with a super critical nonlinearity f ðuÞ ¼ P j00 f j ðuÞ, and f j ðuÞ are such that f j ðuÞ ¼ l j juj sj Àj u j , where l j A C,We prove the existence of the scattering operator in the weighted Sobolev spaces.