Nonlinear Schrödinger equation with delay and its regularization

The report will be devoted to the properties of initial-boundary value problem for a nonlinear Schro¨dinger equation including terms with delay of time argument. The influence of the delay in the potential or source term on the changing of norm and energy is studied. The conditions of global existence or arising of gradient blow up phenomenon are obtained. The relation of the gradient blow up phenomenon with the self-focusing and the destruction of pure quantum state are described ( Grekhneva A.D., Sakbaev V.Zh. Dynamics of a Set of Quantum States Generated by a Nonlinear Liouville–von Neumann Equation// Comp. Math. Math. Phys. 2020. V. 60 (8). P. 1337-1347).