相关论文: The integrability of the 2-Toda lattice on a simpl…
We define the periodic Full Kostant-Toda on every simple Lie algebra, and show its Liouville integrability. More precisely we show that this lattice is given by a Hamiltonian vector field, associated to a Poisson bracket which results from…
We define an integrable hamiltonian system of Toda type associated with the real Lie algebra $\so{p}{q}$. As usual there exists a periodic and a non-periodic version. We construct, using the root space, two Lax pair representations and the…
The theory of Poisson-Lie groups and Lie bialgebras plays a major role in the study of one dimensional integrable systems; many families of integrable systems can be recovered from a Lax pair which is constructed from a Lie bialgebra…
Darboux integrability of semidiscrete and discrete 2D Toda lattices corresponding to Lie algebras of A and C series is proved.
In this article we discuss a weaker version of Liouville's theorem on the integrability of Hamiltonian systems. We show that in the case of Tonelli Hamiltonians the involution hypothesis on the integrals of motion can be completely dropped…
We establish the Liouville integrability of the differential equation $\dot S(t)= [N,S^2(t)],$ recently considered by Bloch and Iserles. Here, $N$ is a real, fixed, skew-symmetric matrix and $S$ is real symmetric. The equation is realized…
A fairly complete list of Toda-like integrable lattice systems, both in the continuous and discrete time, is given. For each system the Newtonian, Lagrangian and Hamiltonian formulations are presented, as well as the 2x2 Lax representation…
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in the special case when A is a Toepliz matrix where all off-diagonal entries…
In this paper, we give the necessary and sufficient conditions of the integrability of relative Rota-Baxter Lie algebras via double Lie groups, matched pairs of Lie groups and factorization of diffeomorphisms respectively. We use the…
The aim of this work is focused on linearizing and found the Lax Pairs of the algebraic complete integrability (a.c.i) Toda lattice associated with the twisted affine Lie algebra \(a_4^{\left(2\right)}\). Firstly, we recall that our case of…
The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this…
The general solution of the two-dimensional integrable generalization of the f-Toda chain with fixed ends is explicitly presented in terms of matrix elements of various fundamental representations of the SL(n|n-1) supergroup. The dominant…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We…
This paper is mainly a review of the multi--Hamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include master symmetries,…
In analogy with the Liouville case we study the $sl_3$ Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete $W_3$ algebra. We define an integrable system with respect to the latter and…
In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we…
One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the…
For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact"…
R-matrix is explicitly constructed for simplest representations of the Ding-Iohara-Miki algebra. The calculation is straightforward and significantly simpler than the one through the universal R-matrix used for a similar calculation in the…