This paper addresses the existence of codimension one stable manifolds forthe pseudo-conformal blow-up solution for critical one-dimensional NLS. By thework of Perelman and Merle, Raphael, the blow-up rate of these solutions is farfrom the generic one. However, Bourgain,Wang and Perelman formulated thepossibility of codimension one stable manifolds for the non-generic blow-upsolutions. This paper established the existence of such manifolds, albeit onlyin the measurable category.
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