Large data local well-posedness for a class of KdV-type equations

In this article we consider the Cauchy problem with large initial data for an equation of the form (\partial_t+\partial_x^3)u=F(u,u_x,u_{xx}) where F is a polynomial with no constant or linear terms. Local well-posedness was established in weighted Sobolev spaces by Kenig-Ponce-Vega. In this paper we prove local well-posedness in a translation invariant subspace of H^s by adapting the result of Marzuola-Metcalfe-Tataru on quasilinear Schrodinger equations.