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We consider the one dimensional nonlinear Schrödinger equation iut þ uxx=2 1⁄4 f ðuÞ, x A R, t > 0, uð0; xÞ 1⁄4 u0ðxÞ, x A R, with a super critical nonlinearity f ðuÞ 1⁄4 P j00 fjðuÞ, and fjðuÞ are such that fjðuÞ 1⁄4 lj juj sj u j , where lj A C , sj > 3: We prove the existence of the scattering operator in the weighted Sobolev spaces.

Scattering Problem for the Supercritical Nonlinear Schrödinger Equation in 1d