From Toda to KdV. (22nd June 2015)
- Record Type:
- Journal Article
- Title:
- From Toda to KdV. (22nd June 2015)
- Main Title:
- From Toda to KdV
- Authors:
- Bambusi, D
Kappeler, T
Paul, T - Abstract:
- Abstract: For periodic Toda chains with a large number N of particles we consider states which are N −2 -close to the equilibrium and constructed by discretizing arbitrary given C 2 −functions with mesh size N −1 . Our aim is to describe the spectrum of the Jacobi matrices L N appearing in the Lax pair formulation of the dynamics of these states as N → ∞. To this end we construct two Hill operators H ± —such operators come up in the Lax pair formulation of the Korteweg–de Vries equation—and prove by methods of semiclassical analysis that the asymptotics as N → ∞ of the eigenvalues at the edges of the spectrum of L N are of the form where are the eigenvalues of H ± . In the bulk of the spectrum, the eigenvalues are o ( N −2 )-close to the ones of the equilibrium matrix. As an application we obtain asymptotics of a similar type of the discriminant, associated to L N .
- Is Part Of:
- Nonlinearity. Volume 28:Number 7(2015:Jul.)
- Journal:
- Nonlinearity
- Issue:
- Volume 28:Number 7(2015:Jul.)
- Issue Display:
- Volume 28, Issue 7 (2015)
- Year:
- 2015
- Volume:
- 28
- Issue:
- 7
- Issue Sort Value:
- 2015-0028-0007-0000
- Page Start:
- 2461
- Page End:
- 2496
- Publication Date:
- 2015-06-22
- Subjects:
- toda lattice -- KdV equation -- semiclassical limit
37K10 -- 70F45 -- 81Q20
Nonlinear theories -- Periodicals
Mathematical analysis -- Periodicals
Mathematical analysis
Nonlinear theories
Periodicals
515 - Journal URLs:
- http://www.iop.org/Journals/no ↗
http://iopscience.iop.org/0951-7715/ ↗
http://ioppublishing.org/ ↗ - DOI:
- 10.1088/0951-7715/28/7/2461 ↗
- Languages:
- English
- ISSNs:
- 0951-7715
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - BLDSS-3PM
British Library STI - ELD Digital store - Ingest File:
- 10065.xml