Evolution of Weyl functions and initial-boundary value problems

Abstract

This review is dedicated to some recent results on Weyl theory, inverse problems, evolution of the Weyl functions and applications to integrable wave equations in a semistrip and quarter-plane. For overdetermined initial-boundary value problems, we consider some approaches, which help to reduce the number of the initial-boundary conditions. The interconnections between dynamical and spectral Dirac systems, between response and Weyl functions are studied as well.

This paper is a review of recent results, including results from our papers: arXiv:1112.1325, arXiv:1401.3605, arXiv:1403.8111, arXiv:1405.3500 and arXiv:1507.00032

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