Action of a scattering map on weighted Sobolev spaces in the plane

TL;DR

This paper investigates a scattering map related to the Davey-Stewartson II equation, demonstrating its invertibility between specific weighted Sobolev spaces, which advances understanding in nonlinear scattering theory.

Contribution

It establishes the invertibility of a scattering map within weighted Sobolev spaces, providing new insights into the mathematical structure of the Davey-Stewartson II equation.

Findings

Scattering map is invertible between weighted Sobolev spaces

Results apply to the $ar ext{d}$-approach in scattering theory

Enhances understanding of nonlinear PDEs in mathematical physics

Abstract

We consider a scattering map that arises in the $\bar \partial $-approach to the scattering theory for the Davey-Stewartson II equation and show that the map is an invertible map between certain weighted $L^2$ Sobolev spaces.