Math. Model. Nat. Phenom.
Volume 11, Number 2, 2016Spectral problems
|Page(s)||111 - 132|
|Published online||21 March 2016|
Evolution of Weyl Functions and Initial-Boundary Value Problems
Vienna University of Technology, Austria
⋆ Corresponding author.
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.
Mathematics Subject Classification: 34A55 / 34B20 / 35F46 / 35F61 / 35G61 / 35N30 / 37K15
Key words: Weyl function / inverse problem / nonlinear integrable equation / zero curvature representation / compatibility condition / initial-boundary value problem / evolution of the Weyl function / initial conditions / boundary conditions / quasi-analytic function / spectral Dirac system / dynamical Dirac system / response function
© EDP Sciences, 2016
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