Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications
Classical Analysis and ODEs
2018-03-20 v1 Mathematical Physics
Dynamical Systems
math.MP
Spectral Theory
Abstract
We introduce GBDT version of Darboux transformation for symplectic and Hamiltonian systems as well as for Shin-Zettl systems and Sturm-Liouville equations. These are the first results on Darboux transformation for general-type Hamiltonian and for Shin-Zettl systems. The obtained results are applied to the corresponding transformations of the Weyl-Titchmarsh functions and to the construction of explicit solutions of dynamical symplectic systems, of two-way diffusion equations and of indefinite Sturm-Liouville equations. The energy of the explicit solutions of dynamical systems is expressed (in a quite simple form) in terms of the parameter matrices of GBDT.
Keywords
Cite
@article{arxiv.1608.02348,
title = {Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:1608.02348},
year = {2018}
}
Comments
Section 7 of this paper is related to our recent paper arXiv:1603.08709