A 2-component Camassa-Holm equation, Euler-Bernoulli Beam Problem and Non-Commutative Continued Fractions
Abstract
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral deformations of the beam problem is formulated; (2) a reformulation of the matrix string problem in terms of a certain compact operator is used to obtain basic spectral properties of the inhomogeneous matrix string problem with Dirichlet boundary conditions; (3) the inverse problem is solved for the special case of a discrete Euler-Bernoulli beam. The solution involves a non-commutative generalization of Stieltjes' continued fractions, leading to the inverse formulas expressed in terms of ratios of Hankel-like determinants.
Cite
@article{arxiv.2011.05964,
title = {A 2-component Camassa-Holm equation, Euler-Bernoulli Beam Problem and Non-Commutative Continued Fractions},
author = {Richard Beals and Jacek Szmigielski},
journal= {arXiv preprint arXiv:2011.05964},
year = {2021}
}