Well-posedness of the Cauchy problem for the Hirota equation in Sobolev spaces image Original Research Article

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