Discrete Fourier restriction associated with KdV equations

Abstract

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg–de Vries equation with nonlinear term $F\left(u\right){\partial }_{x}u$ provided $F\in C^5$ and the initial data $\varphi \in H^s$ with $s>1∕2$.