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The inverse spectral problem for the discrete cubic string
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.ORCID iD: 0000-0003-4137-8272
2007 (English)In: Inverse Problems, ISSN 0266-5611, Vol. 23, no 1, 99-121 p.Article in journal (Refereed) Published
Abstract [en]

Given a measure m on the real line or a finite interval, the cubic string is the third-order ODE - ′′′ ≤ zm where z is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a non-self-adjoint 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 formulae for the measure m are given. These formulae generalize Stieltjes' formulae used by Krein in his study of the corresponding second-order ODE -″ ≤ zm. © 2007 IOP Publishing Ltd.

Place, publisher, year, edition, pages
2007. Vol. 23, no 1, 99-121 p.
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URN: urn:nbn:se:liu:diva-39442DOI: 10.1088/0266-5611/23/1/005Local ID: 48398OAI: diva2:260291
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-11-14

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