Large $|k|$ behavior for the reflection coefficient for Davey-Stewartson II equations

TL;DR

This paper extends the analysis of complex geometric optics solutions for the Davey-Stewartson II equations to the reflection coefficient, providing improved asymptotic relations for large spectral parameter values.

Contribution

It introduces new asymptotic relations for the reflection coefficient in the context of large spectral parameters for compactly supported potentials.

Findings

Derived improved asymptotic formulas for the reflection coefficient.

Extended previous results to include the reflection coefficient.

Applicable to potentials with smooth, strictly convex boundaries.

Abstract

The study of complex geometric optics solutions to a system of d-bar equations appearing in the context of electrical impedance tomography and the scattering theory of the integrable Davey-Stewartson II equations for large values of the spectral parameter $k$ in \cite{KlSjSt20} is extended to the reflection coefficient. For the case of potentials $q$ with compact support on some domain $\Omega$ with smooth strictly convex boundary, improved asymptotic relations are provided.