Analysis and Applied Mathematics Seminar
Zhiwu Lin
Georgia Institute of Technology
Invariant manifolds for supercritical KDV equation
Abstract: Consider
generalized KDV equations with a power non-linearity (u^p)_x. These KDV
equations have solitary traveling waves, which are linearly unstable
when p>5 (supercritical case). Jointly with Jiayin Jin and Chongchun
Zeng, we constructed invariant manifolds (stable, unstable and center)
near the orbit of the unstable traveling waves in the energy space. In
particular, the local uniqueness and orbital stability of the center
manifold is obtained. These invariant manifolds give a complete
description of the dynamics near unstable traveling waves.
Monday March 27, 2017 at 4:00 PM in SEO 636