Singular solutions of the subcritical nonlinear Schrödinger equation

We show that the subcritical dd-dimensional nonlinear Schrödinger equation iψt+Δψ+|ψ|2σψ=0, where 1<σd<21<σd<2, admits smooth solutions that become singular in LpLp for p∗

► Explicit solutions of the subcritical NLS that become singular in Lp are found.
► The solutions are not in H1.
► The stability of these solutions is still open.