Kenji Nakanishi - Global Dynamics Around and Away From Solitons
Explore global dynamics in nonlinear dispersive partial differential equations, focusing on solitons in this 39-minute lecture by Kenji Nakanishi for the International Mathematical Union. Delve into the nonlinear Klein-Gordon equation, examining solutions slightly above ground state energy and in the energy space. Investigate stable and unstable solitons, using the nonlinear Schrödinger equation as a model for two-soliton systems. Learn about mass-energy restrictions and global dynamics with stable/unstable solitons. Analyze two-soliton interactions in the nonlinear Klein-Gordon equation with constant damping, discussing soliton instability. Conclude by considering open questions regarding three-soliton systems and soliton mergers, providing insights into cutting-edge research in nonlinear dynamics.