Related papers: Generalized fermionic discrete Toda hierarchy
In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric construction of a commutative family of vector fields on compact…
The generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set of generalized string equations. These generalized string…
The paper concerns the topology of an isospectral real smooth manifold for certain Jacobi element associated with real split semisimple Lie algebra. The manifold is identified as a compact, connected completion of the disconnected Cartan…
In this manuscript, a modified $R_I$ type recurrence relation is considered whose recurrence coefficients are perturbed by addition or multiplication of a constant. The perturbed system of recurrence coefficients is represented by Toda…
A new Poisson structure on a subspace of the Kupershmidt algebra is defined. This Poisson structure, together with other two already known, allows to construct a trihamiltonian recurrence for an extension of the periodic Toda lattice with…
In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of…
The extended N=2 supersymmetric Camasa - Holm equation is presented. It is accomplishe by formulation the supersymmeytric version of the Fuchssteiner method. In this framework we use two supersymmetric recursion operators of the N=2,…
It is known that there is a duality between the Davey--Stewartson type coupled systems and a class of integrable two--dimensional Toda type lattices. More precisely, the coupled systems are generalized symmetries for the lattices and the…
The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear…
The objective of this paper is to present some geometric aspects of surfaces associated with theta function solutions of the periodic 2D-Toda lattice. For this purpose we identify the $(N^2-1)$-dimensional Euclidean space with the ${\frak…
A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from…
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 purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a…
It is shown that the Lax pair equation dL/dt = [L,A] can be given a neat tensorial interpretation for finite-dimensional quadratic Hamiltonians. The Lax matrices L and A are shown to arise from third rank tensors on the configuration space.…
We give two formulas for the generalized Hopf invariant and 4-fold Toda brackets which are useful in computations of homotopy groups of spheres.
The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving…
In this paper, we give finite dimensional exponential solutions of the bigraded Toda Hierarchy(BTH). As an specific example of exponential solutions of the BTH, we consider a regular solution for the $(1,2)$-BTH with $3\times 3$-sized Lax…
We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to…
We apply the direct method of obtaining reductions to the Toda hierarchy of equations. The resulting equations form a hierarchy of ordinary differential difference equations, also known as delay-differential equations. Such a hierarchy…
This paper is the first in a forthcoming series of works where the authors study the global asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type $A_n$. The principal issue is the connection formulae between…