The inverse spectral problem for the discrete cubic string
| dc.creator | Kohlenberg, Jennifer | |
| dc.creator | Lundmark, Hans | |
| dc.creator | Szmigielski, Jacek | |
| dc.date | 2006-11-24 | |
| dc.date.accessioned | 2026-07-07T12:53:16Z | |
| dc.date.available | 2026-07-07T12:53:16Z | |
| dc.description | Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-ϕ'''=zmϕ$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-ϕ''=zmϕ$. | |
| dc.description | 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP) | |
| dc.identifier | https://arxiv.org/abs/math/0611745 | |
| dc.identifier | http://arxiv.org/abs/math/0611745 | |
| dc.identifier | Inverse Problems, 23 (February 2007): 99-121 | |
| dc.identifier | doi:10.1088/0266-5611/23/1/005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223567 | |
| dc.subject | Spectral Theory | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.subject | 34B05 (Primary); 34A55, 34B20, 41A28 (Secondary) | |
| dc.title | The inverse spectral problem for the discrete cubic string | |
| dc.type | text |