Related papers: 2D Toda chain and associated commutator identity
It is shown that commutator identities on associative algebras generate solutions of linearized integrable equations. Next, a special kind of the dressing procedure is suggested that in a special class of integral operators enables to…
This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…
A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented.…
We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations…
A sequence of solutions to the equation of symmetry for the continuous Toda chain in $1+2$ dimensions is represented in explicit form. This fact leads to the supposition that this equation is completely integrable.
We show that the identity is the sum of two commutators in the algebra of all operators affiliated with a von Neumann algebra of type II$_1$, settling a question, in the negative, that had puzzled a number of us.
We prove that with a $(2+1)$-dimensional Toda type system are associated algebraic skeletons which are (compatible assemblings) of particle-like Lie algebras of dyons and triadons type. We obtain trix-coaxial and dyx-coaxial Lie algebra…
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…
We conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators for quantum Toda chains. In particular we propose a…
We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and,…
The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_\infty$, $B_\infty$ and $C_\infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$,…
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…
We have derived a non-abelian analog for the two-dimensional discrete Toda lattice which possesses solutions in terms of quasideterminants and admits Lax pairs of different forms. Its connection with non-abelian analogs for several…
We propose a new integrable N=2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax--pair…
The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum operators of the corresponding quantum integrable models.…
Discrete analogs of the finite and affine Toda field equations are found corresponding to the Lie algebras of series $C_N$ and $\tilde{C_N}$. Their Lax pairs are represented.
In this paper, we present a complete classification of 2-dimensional endo-commutative straight algebras of type II$_1$ over any field. An endo-commutative algebra is a non-associative algebra in which the square mapping preserves…
We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the first and second kind. We propose a ternary commutator,…
We propose a compact and explicit expression for the solutions of the complex Toda chains related to the classical series of simple Lie algebras g. The solutions are parametrized by a minimal set of scattering data for the corresponding Lax…
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…