Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity I: Basic theory

Justin Holmer, Chang Liu

We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, $$(\delta \text{NLS})i{\partial }_t\psi +{\partial }_x^2\psi +\delta |\psi {|}^{p-1}\psi =0,$$ where $\delta =\delta (x)$ is…