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We consider the $L^{2}$-critical quintic focusing nonlinear Schr\"odingerequation (NLS) on ${\bf R}$. It is well known that $H^{1}$ solutions of theaforementioned equation blow up in finite time. In higher dimensions, for$H^{1}$ spherically symmetric blow-up solutions of the $L^{2}$-criticalfocusing NLS, there is a minimal amount of concentration of the $L^{2}$-norm(the mass of the ground state) at the origin. In this paper we prove theexistence of a similar phenomenon for the one-dimensional case and rougherinitial data, $(u_{0}\in H^{s}, s<1)$, without any additional assumption.

Mass Concentration Phenomenon for the Quintic Nonlinear Schrödinger Equation in One Dimension