English

The Deift Conjecture: A Program to Construct a Counterexample

Mathematical Physics 2021-11-19 v1 Analysis of PDEs Complex Variables Dynamical Systems Functional Analysis math.MP

Abstract

We describe a program to construct a counterexample to the Deift conjecture, that is, an almost periodic function whose evolution under the KdV equation is not almost periodic in time. The approach is based on a dichotomy found by Volberg and Yuditskii in their solution of the Kotani problem, which states that there exists an analytic condition that distinguishes between almost periodic and non-almost periodic reflectionless potentials with resolvent set given by a Widom domain.

Cite

@article{arxiv.2111.09345,
  title  = {The Deift Conjecture: A Program to Construct a Counterexample},
  author = {David Damanik and Milivoje Lukić and Alexander Volberg and Peter Yuditskii},
  journal= {arXiv preprint arXiv:2111.09345},
  year   = {2021}
}

Comments

41 pages

R2 v1 2026-06-24T07:42:40.069Z