The fifth order KP–II equation on the upper half–plane

Abstract

In this paper, we study the fifth order Kadomtsev–Petviashvili II (KP–II) equation on the upper half–plane $U=\{(x,y)\in \mathbb R^2: y>0\}$. In particular, we obtain low regularity local well–posedness using the restricted norm method of Bourgain and the Fourier–Laplace method of solving initial and boundary value problems. Moreover, we prove that the nonlinear part of the solution is in a smoother space than the initial data.