Venue: Global dynamics beyong the ground state energy for nonlinear dispersive equations

Speaker: Profrssor Kenji Nakanishi (Kyoto University)

Time: 17 February 2012,14:00-15:00

Location: Room 201, Sir Run Run Shaw Business Adminisration Building, Yuquan Campus

Abstract:

I will survey the joint work with Wilhelm Schlag and Joachim Krieger. Our goal is to classify and predict global behavior of solutions for nonlinear dispersive equations, such as the nonlinear Schrodinger and Klein-Gordon equations. Since those equations have various solutions including scattering, solitons, and blow-up, we should expect that dynamical description of general solutions would be very complicated. However, by restricting the energy below a threshold slightly above the ground state, we are able to classify the global behavior into 9 sets, which include scattering, solitons and blow-up, as well as transitions among them from negative to positive times. It is not talking about possibilities, but we have rather concrete description for each of the 9 sets as manifolds in the energy space, with at most a few codimensions. The key idea is to preclude orbits departing from and returning to a small neighborhood of the ground state solitons.