Zhiwu Lin : Invariant manifolds for supercritical KDV equation

Posted by Mimi Dai , part of the Analysis and Applied Mathematics Seminar.

At

March 27, 2017, 4 p.m.

In

SEO 636

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.