Toda lattice — 1 articles found.
Almost Periodicity in Time of Solutions of the Toda Lattice
Ilia Binder,Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Toronto, Ontario, Canada M5S 2E4;
e-mail: ilia@math.toronto.eduDavid 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
PDF(click to download): Almost Periodicity in Time of Solutions of the Toda Lattice