Research

My research subject is mathematical analysis of partial differential equations, mainly of those called nonlinear wave equations or nonlinear dispersive equations, which describe space-time evolution of waves with strong interactions, arising in several physical contexts, such as plasma, superfluid, and water waves. Depending on the competition between the dispersion and the nonlinear interactions, a single equation can typically produce many types of solutions, such as scattering, solitons, and blow-up. In recent years, the ultimate goal of my research has been to grasp the entire picture of all general solutions to some equations. I am particularly interested in understanding and describing possible transitions in time between various types of solutions, as well as in the intermediate or threshold solutions in the phase space.