Year: 2025
Type: article
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.
Source: Nonlinearity
Authors: Peter A Perry, Camille Schuetz
Institutions: University of Kentucky, University of Wisconsin–Platteville
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: Simons Foundation
Award: G8854400422
OpenAlex ID: W4408415327