# On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory.

@article{Sakhnovich2020OnAC, title={On a class of canonical systems corresponding to matrix string equations: general-type and explicit fundamental solutions and Weyl--Titchmarsh theory.}, author={Alexander L. Sakhnovich}, journal={arXiv: Classical Analysis and ODEs}, year={2020} }

An important representation of the general-type fundamental solutions of the canonical systems corresponding to matrix string equations is established using linear similarity of a certain class of Volterra operators to the squared integration. Explicit fundamental solutions of these canonical systems are also constructed via the GBDT version of Darboux transformation. Examples and applications to dynamical canonical systems are given. Explicit solutions of the dynamical canonical systems are… Expand

#### 4 Citations

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

- Mathematics, Physics
- 2021

We consider canonical systems (with 2p×2p Hamiltonians H(x) ≥ 0), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh–Weyl and spectral matrix… Expand

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

- Mathematics, Physics
- 2021

We obtain high energy asymptotics of Titchmarsh-Weyl functions of the generalised canonical systems generalising in this way a seminal Gesztesy-Simon result. The matrix valued analog of the amplitude… Expand

Matrix roots and Darboux matrices for generalised canonical systems depending rationally on the spectral parameter

- Mathematics, Physics
- 2021

We study matrix roots with certain commutation properties and their application to the explicit construction of Darboux matrices in the framework of the GBDT version of Bäcklund-Darboux… Expand

On the classes of explicit solutions of Dirac, dynamical Dirac and Dirac–Weyl systems with non-vanishing at infinity potentials, their properties and applications

- Mathematics
- 2020

Abstract We construct explicitly potentials, Darboux matrix functions and corresponding solutions of Dirac, dynamical Dirac and Dirac–Weyl systems using generalised Backlund-Darboux transformation… Expand

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