De Toda à KdV - Mathematics > Analysis of PDEsReport as inadecuate

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Abstract: We consider the large number of particles limit of a periodic Toda latticefor a family of initial data close to the equilibrium state. We show that eachof the two edges of the spectra of the corresponding Jacobi matrices is up toan error, determined by the spectra of two Hill operators, associated to thisfamily. We then show that the spectra of the Jacobi matrices remain almostconstant when the matrices evolve along the two limiting KdV equations. Finallywe prove that the Toda actions, when appropriately renormalized, converge tothe ones of KdV .

Author: Dario Bambusi, Thomas Kappeler, Thierry Paul DMA


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