My research subject is nonlinear partial differential equations. Especially, I am interested in the global behavior of the solutions to nonlinear dispersive equations or nonlinear wave equations.
Dispersive equations describe the dispersion phenomena of waves and are basic equations in quantum physics. For example, Schrödinger equation and Klein-Gordon equation are typical dispersive equations, which appear in quantum physics or relativistic quantum field theory. Wave equations express the properties of motion in waves. Considering nonlinear interactions between particles,
we can treat various physical phenomena, for example, optics, superconductivity, and Bose-Einstein condensate, by the nonlinear dispersive or wave equations. Nonlinear dispersive or wave equations have two properties.
One is dispersion and the other is nonlinearity. They conflict each other. Thus, there are so many behaviors of the solutions. I study this subject to find all behavior.