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Global bounds for the cubic nonlinear Schrödinger equation (NLS) in one space dimension (1404.7581v2)
Published 30 Apr 2014 in math.AP
Abstract: This article is concerned with the small data problem for the cubic nonlinear Schr\"odinger equation (NLS) in one space dimension, and short range modifications of it. We provide a new, simpler approach in order to prove that global solutions exist for data which is small in $H{0,1}$. In the same setting we also discuss the related problems of obtaining a modified scattering expansion for the solution, as well as asymptotic completeness.