Seminar on nonlinear problems of PDE and mathematical physics «Dynamics of the quantum state space which is generated by Cauchy problem for nonlinear Schrodinger equation»

Speaker:  D.Sc.,  Professor Sakbaev V. Zh. (Moscow Institute of Physics and Technology, Moscow)

Title of the talk: «Dynamics of the quantum state space which is generated by Cauchy problem for nonlinear Schrodinger equation».

Abstract: We study the Cauchy problem for nonlinear Schrodinger equation whose coordinate space is the segment. The local unique solvability of Cauchy problem, the effects of global existence and arising of gradient blow up of the solution are investigated. The relationship between the properties of solutions such us gradient blow up, self-focusing and the destruction of the pure quantum state is obtained. The continuations of the dynamical mapping across the arising of gradient blow up are studied in the space of quantum states.