February 25, 2022

About the speaker

Dr. Guoping Zhang is an associate professor of mathematics at Morgan State University. He received his PhD in applied mathematics from the University of Tokyo in Japan. Dr. Zhang’s research interest is nonlinear partial differential equations such as Schrödinger, Camassa-Holm, Degasperis-Procesi equations etc. and their applications to mathematical imaging. Currently he is focusing on the study of standing waves and well-posedness of the discrete nonlinear Schrödinger equations.

Initial value problem of the discrete nonlinear Schrödinger equation with complex potential

The discrete nonlinear Schrödinger equation (DNLS) is one of the most important and popular discrete models in Nonlinear Mathematical Physics with a huge variety of applications. For instance, we mention nonlinear wave transmission in discrete media, propagation of localized pulses in coupled wave guides and optical fibers, and modeling Bose-Einstein condensates. In this talk I will present our recent research results on the time dependent discrete nonlinear Schrödinger equation with complex, not necessarily bounded, potential and sufficiently general nonlinearity on a multi dimensional lattice. Under natural assumptions we proved the global well-posedness in weighted l^2 spaces. In the dissipative case we obtained a result on the existence of global compact attractor in such spaces.