On the solution of the inverse problem for a class of canonical systems corresponding to matrix string equations

Abstract

We consider canonical systems (with $2p\times 2p$ Hamiltonians $H(x)\ge 0$), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related $S$-nodes. Procedures for solving inverse problems are given.

This is the concluding paper in our series of three articles dedicated to canonical systems related to matrix string equations. Two previous articles appeared in arXiv as well: see arXiv:2010.05217 and arXiv:2103.03203

References in corpus (6)

• Inverse Scattering Transform for the Camassa-Holm equation
• Generalised Fourier transform for the Camassa-Holm hierarchy
• Periodic solutions of symmetric Hamiltonian systems
• On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory
• On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications
• Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions

Cited by in corpus (1)

• Generalised canonical systems related to matrix string equations: corresponding structured operators and high-energy asymptotics of the Weyl functions