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- Title
On Isospectral Deformations of an Inhomogeneous String.
- Authors
Colville, Kale; Gomez, Daniel; Szmigielski, Jacek
- Abstract
In this paper we consider a class of isospectral deformations of the inhomogeneous string boundary value problem. The deformations considered are generalizations of the isospectral deformation that has arisen in connection with the Camassa-Holm equation for the shallow water waves. It is proved that these new isospectral deformations result in evolution equations on the mass density whose form depends on how the string is tied at the endpoints. Moreover, it is shown that the evolution equations in this class linearize on the spectral side and hence can be solved by the inverse spectral method. In particular, the problem involving a mass density given by a discrete finite measure and arbitrary boundary conditions is shown to be solvable by Stieltjes' continued fractions.
- Subjects
DEFORMATIONS (Mechanics); INHOMOGENEOUS materials; NUMERICAL solutions to boundary value problems; NUMERICAL solutions to evolution equations; LINEAR systems
- Publication
Communications in Mathematical Physics, 2016, Vol 348, Issue 3, p771
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-016-2711-y