Discrete Fourier restriction associated with KdV equations (Q371181)

The authors consider a discrete restriction associated with the KdV equations. Some new Strichartz estimates are obtained. Strichartz estimates are closely connected to the discrete restriction problem. They also establish the local well-posedness for the periodic generalized KdV equation with nonlinear term \(F(u) \partial_x u\) provided that \(F\in C^5\) and that the initial data \(\phi\) is in \(H^s\) with \(s>1/2\). It is a generalization of previous results where the nonlinear term is \(u^k u_x (k>2)\).