Abstract

For the critical one-dimensional nonlinear Schrödinger equation, we construct blow-up solutions that concentrate a soliton at the origin at the conformal blow-up rate, with a nonflat blow-up profile. More precisely, we obtain a blow-up profile that equals $\left|x\right|+i\kappa x^2$ near the origin, where $\kappa$ is a universal real constant. Such profile differs from the flat profiles obtained in the same context by Bourgain and Wang in 1997.

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