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

2025/10/13 by Frank, Rupert L., Read, Larry · 3 citations
#35A22 #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Primary: 35P25 #Secondary: 37K15 #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2510.11403

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.

Cited by

• Global well-posedness for intermediate NLS with nonvanishing conditions at infinity
• Scattering of the defocusing Calogero--Moser derivative nonlinear Schrödinger equation
• Small-data L² theory for the intermediate NLS and the Calogero--Moser derivative NLS

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