Solutions to the fifth-order KP II equation scatter

Abstract The fifth-order KP II equation describes dispersive long waves in two space dimensions. In this paper we show that solutions with small initial data scatter to solutions of the associated linear fifth-order equation. In particular, we establish the existence of nonlinear wave operators mapping the initial data to scattering asymptotes, and show that the nonlinear wave operators have inverses in a neighborhood of the origin. Our paper uses techniques developed for the third-order KP II equation by Hadac, Herr, and Koch.