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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation. (English) Zbl 0787.35098
[For part I, cf. the review above.] The author studies the initial value problem for the periodic, in space, Korteweg-de Vries equation and some of its variants $$\partial\sb tu+\partial\sb{xxx}u+u\sp k \partial\sb xu=0,\ u(x,0)=\varphi(x)\quad (k \ge 1),\ u\text{ periodic in } x.$$ It is established a local result by Picard’s theorem, verifying a contracting property for the associated integral equation in a suitable space, mainly using Fourier analysis estimates. Combining the existence of local solutions with the $L\sp 2$- conservation law, it is obtained the global solution (after regularization).

##### MSC:
 35Q55 NLS-like (nonlinear Schrödinger) equations 42B10 Fourier type transforms, several variables
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##### References:
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