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global well-posedness 1integrable systems 1jacobi operators 1spectral theory 1toda lattice 1

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math.SP2026

Asymptotics of Titchmarsh--Weyl functions near the real axis andan application to the KdV hierarchy

Shuo Zhang

We establish high-energy asymptotic expansions of Titchmarsh--Weyl functions for one-dimensional Schrödinger and Dirac operators in regions whose boundaries approach the spectrum a…

math.SP2026

Toda flow with unbounded initial data

Shinichi Kotani, Jiahao Xu, Shuo Zhang

A Toda flow is constructed starting from a certain class of unbounded initial conditions including sequences growing with power order of less than 1. Unbounded ergodic sequences ar…