35B15 — 1 articles found.

Almost Periodicity in Time of Solutions of the Toda Lattice

C. R. Math. Rep. Acad. Sci. Canada Vol. 40 (1) 2018, pp. 1-28
Vol.40 (1) 2018
Ilia Binder; David Damanik; Milivoje Lukic; Tom VandenBoom Details
(Received: 2017-11-11 , Revised: 2017-12-21 )
(Received: 2017-11-11 , Revised: 2017-12-21 )

Ilia Binder,Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Toronto, Ontario, Canada M5S 2E4;
e-mail: ilia@math.toronto.edu

David Damanik,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: damanik@rice.edu

Milivoje Lukic,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: milivoje.lukic@rice.edu

Tom VandenBoom,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: tvandenboom@rice.edu

Abstract/Résumé:

We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous and has a spectrum satisfying a Craig-type condition, and show the boundedness and almost periodicity in time and space of solutions.

On étudie un problème de Cauchy pour le système Toda avec des conditions initiales presque périodiques. On considère des conditions initiales pour lesquelles l’opérateur de Jacobi associé est absolument continu et a un spectre qui satisfait à une condition à la façon de Craig, afin de montrer que les solutions sont bornées et presque périodiques dans la variable spatiale aussi que temporelle.

Keywords: Toda lattice, almost periodic Jacobi operators

AMS Subject Classification: Almost periodic solutions, Completely integrable systems; integrability tests; bi-Hamiltonian structures; hierarchies (KdV; KP; Toda; etc.), Jacobi (tridiagonal) operators (matrices) and generalizations 35B15, 37K10, 47B36

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