Related papers: Unstable higher Toda brackets II
A detailed consideration of the maximally nonabelian Toda systems based on the classical semisimple Lie groups is given. The explicit expressions for the general solution of the corresponding equations are obtained.
We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which…
We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…
The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a…
The discrete Toda lattice preserves the eigenvalues of tridiagonal matrices, and convergence of dependent variables to the eigenvalues can be proved under appropriate conditions. We show that the ultradiscrete Toda lattice preserves…
An N=(2|2) superfield formulation of the N=(1|1) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented.
In this paper, we firstly construct a weakly coupled Toda lattices with indefinite metrics which consist of $2N$ different coupled Hamiltonian systems. Afterwards, we consider the iso-spectral manifolds of extended tridiagonal Hessenberg…
We construct solutions of an infinite Toda system and an analogue of the Painlev'e II equation over noncommutative differential division rings in terms of quasideterminants of Hankel matrices.
This paper is a continuation of the papers [2,3,4,5,6]. In this paper the osculating spaces of arbitrary order of a manifold embedded in Euclidean space are considered. A better estimation of their dimensions as well as the description of…
The Toda lattice is a model of nonlinear wave equations allowing exact soliton solutions. It is realized by an electric circuit made of a transmission line with variable capacitance diodes and inductors. It has been generalized to the…
A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…
Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an…
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is…
A classification of (super) $W$ algebras arising from non Abelian Toda and super Toda theories is presented. This classification is based on the $Sl(2)$ or $OSp(1|2)$ sub(super)algebras of the simple Lie (super)algebra underlying the model.…
This article is the second chapter of a two-part series dedicated to the mathematical study of the higher-spin symmetry enjoyed by the $\mathfrak{sl}_3$ boundary Toda Conformal Field Theory. Namely, based on a probabilistic definition of…
A simple procedure to enumerate all Toda systems associated with complex classical Lie groups is given.
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
We propose that stable boson stars generically fall within an infinite-parameter family of solutions that oscillate on any number of non-commensurate frequencies. We numerically construct two-frequency solutions and explore their parameter…