Evolution of Weyl functions and initial-boundary value problems

2015/07/31 by Alexander Sakhnovich
Mathematics · Physics and Astronomy · #math-ph #math.AP #math.CA #math.DS #math.MP #math.SP #msc:34A55 #msc:34B20 #msc:35F46 #msc:35F61 #msc:35G61 #msc:35N30 #msc:37K15

paper · pdf · doi:10.1051/mmnp/201611209

published as Math. Model. Nat. Phenom., 11:2 (2016) 111-132 · 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

arxiv created 2015/07/31 · arxiv updated 2016/11/03

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.

Citations

• Skew-self-adjoint Dirac systems with a rectangular matrix potential: Weyl theory, direct and inverse problems
• Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions
• Weyl functions and the boundary value problem for a matrix nonlinear Schrödinger equation on a semi-strip
• Initial Value Problems for Integrable Systems on a Semi-Strip
• Dynamical and spectral Dirac systems: response function and inverse problems