The generalized Zakharov-Kuznetsov (ZK) equation is a higher dimensional version of the generalized Korteweg-de Vries (gKdV) equation. We prove sharp pointwise decay estimates for the linear part of ZK, give applications to linearized ZK solutions and some applications to well-posedness and soliton stability problems.

This is the first in a series of two talks; the second will be given by Svetlana Roudenko.