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In this paper, we consider a discrete restriction associated with KdVequations. Some new Strichartz estimates are obtained. We also establish thelocal well-posedness for the periodic generalized Korteweg-de Vries equationwith nonlinear term $ F(u)\p_x u$ provided $F\in C^5$ and the initial data$\phi\in H^s$ with $s>1/2$.

Discrete Fourier restriction associated with KdV equations