Mass-critical focusing nonlinear Schrödinger equation ($i{\partial }_{t}u+\Delta u+|u{|}^{4/d}u=0$)

The mass-critical focusing nonlinear Schrödinger equation on ${\mathbb{R}}^d$ isIts scaling $u(t,x)\mapsto {\lambda }^{d/2}u({\lambda }^{2}t,\lambda x)$ preserves the Lebesgue space norm $\Vert u{\Vert }_{L^2}$, which is the conserved mass.