Generation of new exactly solvable potentials of a nonstationary Schrödinger equation

A method for generating integrable potentials of a nonstationary Schrödinger equation (i.e., with time-dependent potential) is developed on the basis of the method of “dressing” of linear differential operators. Potentials that admit separation of the variables generate classes of nonseparating potentials for which the Schrödinger equation has nonlocal symmetry operators.