Corpus ID: 222290511

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

  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},
  • A. Sakhnovich
  • Published 2020
  • Mathematics, Physics
  • arXiv: Classical Analysis and ODEs
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
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Sakhnovich and I.Ya. Roitberg, Inverse Problems and Nonlinear Evolution Equations. Solutions, Darboux Matrices and Weyl–Titchmarsh
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