Gradient Flows on Kač-Moody Algebras and the Periodic Toda Lattice
نویسندگان
چکیده
منابع مشابه
Gradient Flows on Kač-moody Algebras and the Periodic Toda Lattice
Abstract. In this paper, we provide a new formulation for the generalized periodic Toda lattice. Since the work of Kostant, Adler and Symes, it has been known that the Toda lattice is related to the structure of simple Lie algebras. Indeed, the non-periodic and the periodic Toda lattices can be expressed as Hamiltonian systems on coadjoint orbits: the former of a simple Lie group and the latter...
متن کاملNekhoroshev theorem for the periodic Toda lattice.
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) al...
متن کاملStability of the Periodic Toda Lattice in the Soliton Region
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the periodic (and slightly more generally of the quasi-periodic finite-gap) Toda lattice for decaying initial data in the soliton region. In addition, we show how to reduce the problem in the remaining region to the known case without solitons.
متن کاملBirkhoff normal form for the periodic Toda lattice
with potential V (x) = γe + V1x + V2 and γ, δ, V1, V2 ∈ R constants. The Toda lattice has been introduced by Toda [12] and studied extensively in the sequel. It is an FPU lattice, i.e. a Hamiltonian system of particles in one space dimension with nearest neighbor interaction. Models of this type have been studied by Fermi-Pasta-Ulam [FPU]. In numerical experiments they found recurrent features ...
متن کاملGlobal action-angle variables for the periodic Toda lattice
In this paper we construct global action-angle variables for the periodic Toda lattice.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Information and Systems
سال: 2008
ISSN: 1526-7555,2163-4548
DOI: 10.4310/cis.2008.v8.n2.a4