Abstract

We will begin with explaining the Poincare-Dulac normal form idea for canonical nonlinear dispersive equations. Taking an infinite iteration of normal form, we change a nonlinear dispersive equation to an equation with infinite series nonlinear terms,which contain only near-resonant interactions. We will present several results in various settings. Also, a relation to canonical transform will be discussed. Works in the talk are collaborations with Tadahiro Oh, Zihua Guo, Jaywan Chung, and Haewon Yoon.