相关论文: Discrete Toda Field Equations
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.
Difference-difference systems are suggested corresponding to the Cartan matrices of any simple or affine Lie algebra. In the cases of the algebras $A_N$, $B_N$, $C_N$, $G_2$, $D_3$, $A_1^{(1)}$, $A_2^{(2)}$, $D^{(2)}_N$ these systems are…
Differential-difference integrable exponential type systems are studied corresponding to the Cartan matrices of semi-simple or affine Lie algebras. For the systems corresponding to the algebras $A_2$, $B_2$, $C_2$, $G_2$ the complete sets…
It is known that a family of transfer matrix functional equations, the T-system, can be compactly written in terms of the Cartan matrix of a simple Lie algebra. We formally replace this Cartan matrix of a simple Lie algebra with that of an…
The affine Toda field theory is studied as a 2+1-dimensional system. The third dimension appears as the discrete space dimension, corresponding to the simple roots in the $A_N$ affine root system, enumerated according to the cyclic order on…
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…
We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete…
We study the two-dimensional affine Toda field equations for affine Lie algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces…
A consistent set of six integrable discrete and continuous dynamical systems are suggested corresponding to arbitrary affine Lie algebra. The set contains a system of partial differential equations which can be treated as a version 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…
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…
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the…
The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
The paper deals with affine 2-dimensional Toda field theories related to simple Lie algebras of the classical series ${\bf D}_r$. We demonstrate that the complexification procedure followed by a restriction to a specified real Hamiltonian…
Darboux integrability of semidiscrete and discrete 2D Toda lattices corresponding to Lie algebras of A and C series is proved.
Following a prescription of \cite{4} for a solitonic specialization of the general solutions to the (abelian) periodic Toda field theories, we discuss a construction of the soliton solutions for a wide class of two-dimensional completely…
We propose several different types of construction principles for new classes of Toda field theories based on root systems defined on Lorentzian lattices. In analogy to conformal and affine Toda theories based on root systems of semi-simple…
We investigate higher grading integrable generalizations of the affine Toda systems. The extra fields, associated to non zero grade generators, obey field equations of the Dirac type and are regarded as matter fields. The models possess…
Characteristic integrals of Toda field theories associated to simple Lie algebras are presented in the most explicit forms, both in terms of the formulas and in terms of the proofs.