Related papers: Higher Toda Mechanics and Spectral Curves
Given a dynamical system with $m$ independent conserved quantities, we construct a multi-parameter family of new systems in which these quantities evolve monotonically and proportionally, and are replaced by $m-1$ conserved linear…
We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to…
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…
There are different methods of discretizing integrable systems. We consider semi-discrete analog of two-dimensional Toda lattices associated to the Cartan matrices of simple Lie algebras that was proposed by Habibullin in 2011. This…
We study the following generalized $SU(3)$ Toda System $$ \left\{\begin{array}{ll} -\Delta u=2e^u+\mu e^v & \hbox{ in }\R^2\\ -\Delta v=2e^v+\mu e^u & \hbox{ in }\R^2\\ \int_{\R^2}e^u<+\infty,\ \int_{\R^2}e^v<+\infty \end{array}\right. $$…
There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped with an integral gradation. It is explained how the different approaches to these dynamical systems are related by gauge transformations. Combining Gauss…
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…
In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We…
Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…
We extend to the Toda lattice hierarchy the approach of [3, 4] to computation of logarithmic derivatives of tau-functions in terms of the so-called matrix resolvents of the corresponding differ- ence Lax operator. As a particular…
The quasiclassical solution to the extended Toda chain hierarchy, corresponding to the deformation of the simplest Seiberg-Witten theory by all descendants of the dual topological string model, is constructed explicitly in terms of the…
In this paper we introduce a unified approach to Toda field theories which allows us to formulate the classes of $A_n$, $B_n$ and $C_n$ models as unique models involving an arbitrary continuous parameter $\nu$. For certain values of $\nu $,…
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…
Employing a class of generalized connections, we describe certain differential complices $\left(\tilde \Omega^*_{\mathbb{T}}(M), \tilde{\mathbb{d}}^{\mathbb{T}}\right)$ constructed from $\wedge^* \mathbb{T} M$ and study some of their basic…
Various features of the even order poles appearing in the S-matrices of simply-laced affine Toda field theories are analysed in some detail. In particular, the coefficients of first- and second-order singularities appearing in the Laurent…
This paper presents a study of the discrete Toda equation $(\tau_n^t)^2+\tau_{n-1}^t\tau_{n+1}^t=\tau_n^{t-1}\tau_n^{t+1}$, that was introduced in 1977. In this paper, it has been proved that the algebraic solution of the discrete Toda…
Motivated by the realisation of Yang-Baxter equation of 2d Integrable models in the 4d gauge theory of Costello-Witten-Yamazaki (CWY), we study the embedding of integrable 2d Toda field models inside this construction. This is done by using…
We construct a Lagrangian multiform for the class of cyclotomic (rational) Gaudin models by formulating its hierarchy within the Lie dialgebra framework of Semenov-Tian-Shansky and by using the framework of Lagrangian multiforms on…
We discuss the algebro-geometric initial value problem for the Toda hierarchy with complex-valued initial data and prove unique solvability globally in time for a set of initial (Dirichlet divisor) data of full measure. To this effect we…
We compute quantum corrections to soliton masses in affine Toda theories with imaginary exponentials based on the nonsimply-laced Lie algebras $c_n^{(1)}$. We find that the soliton mass ratios renormalize nontrivially, in the same manner as…