Well-posedness of the Cauchy problem for the Hirota equation in Sobolev spaces Hs

The well-posedness of Cauchy problem for the Hirota equation is obtained in Sobolev spaces Hs. Local result is established for initial data in Hs(s⩾14) by using the Fourier restriction norm method. Moreover, the local solution is global for the initial data in Hs(s⩾1) by the generalized trilinear estimates associated with the Fourier restriction norm method.