相关论文: Symmetries of Toda Equations

We give new formulations of the solutions of the field equations of the affine Toda and conformal affine Toda theories on a cylinder and two-dimensional Minkowski space-time. These solutions are parameterised in terms of initial data and…

All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption…

We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…

Let F be a smooth real manifold with a linear connection in the tangent bundle. How can we extend the coefficients of the connection to bi-differential operators that incorporate the original structure at zero order? Take a constant mapping…

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields…

In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…

We present an infinite series of autonomous discrete equations on the square lattice possessing hierarchies of autonomous generalized symmetries and conservation laws in both directions. Their orders in both directions are equal to $\kappa…

We discuss geometrical aspects of Toda Fields generalizing the links between Liouville gravity and uniformization of Riemann surfaces of genus greater than one. The framework is the interplay between the hermitian and the holomorphic…

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector…

The discrete models of the Toda and Volterra chains are being constructed out of the continuum two-boson KP hierarchies. The main tool is the discrete symmetry preserving the Hamiltonian structure of the continuum models. The two-boson…

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…

There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras…

A direct connection between two sequences of points, one of which is generated by seed mutations in the cluster algebra of type $A^{(1)}_1$ and the other by time evolutions of the periodic discrete Toda lattice, is explicitly given. In this…

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the…

The paper is devoted to real Hamiltonian forms of 2-dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral theory of the associated Lax operators. Real Hamiltonian forms are a special type of…

An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…

We consider a deformation of the prolongation operation, defined on sets of vector fields and involving a mutual interaction in the definition of prolonged ones. This maintains the "invariants by differentiation" property, and can hence be…

The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the discrete version of the generalized Toda…

We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and…