Local Solution for the Kadomtsev-Petviashvili Equation in R2

In this paper we obtain results about local existence, uniqueness, regularity, and continuous dependence on the initial data for the solution of the Kadomtsev-Petviashvili equation with positive dispersion in R2 and initial data in Sobolev spaces of order s ≥ 3. Our method uses an approximated problem where the theory of quasi-linear evolution equations is applicable.