Seminar| Institute of Mathematical Sciences
Time: Tuesday, December 23th, 2025,14:00-15:00
Location: RS408, IMS
Speaker: Qingtang Su, CAS
Abstract: It has been known since Zakharov (1968) that deep water waves can be formally approximated by the one-dimensional cubic nonlinear Schrödinger (NLS) equation—a completely integrable system. When rigorously justified, such approximations provide a powerful tool for investigating the long-time dynamics of the WWE. We employ this approach to give the first rigorous proof of nonlinear modulational instability for Stokes waves: joint work with Gong Chen. Additionally, by uncovering a refined structure within the water wave equations, we establish the energy stability of equilibrium states under smooth and localized perturbations, this is joint work with Siwei Wang.