
We shall consider the Cauchy problem for a high dispersion Korteweg-de Vries equation with initial data belonging in Sobolev Spaces or in a class of analytic functions that can be extended holomorphically in a symmetric strip of the complex plane around the x-axis.
This talk is devoted to present results about local well posedness in these classes of functions. Also, we shall discuss global solutions in the analytic spaces and the decay of the radius of spatial analyticity for the solutions as time goes to infinity.
This work is in collaboration with Alex Himonas and Fangchi Yan.