Jost solutions and direct scattering for the continuum Calogero-Moser equation

Abstract

We propose an inverse scattering transform for the continuum Calogero-Moser equation. We give a rigorous treatment of the direct scattering problem by constructing the associated Jost solutions and introducing a distorted Fourier transform, as well as deriving trace formulas for the eigenvalues of the Lax operator.

v2: Improved results, including an unconditional proof of absence of singularly continuous spectrum