An Inhomogeneous, $L^2$-Critical, Nonlinear Schrödinger Equation
An Inhomogeneous, $L^2$-Critical, Nonlinear Schrödinger Equation
An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under L^2 -scaling. The sharp condition for global existence of H^1 -solutions is established, involving the L^2 -norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in …