相关论文: Symmetries of Toda Equations
We first obtain the master symmetry of the differential-difference KP equation.Then we show how this master symmetry, through sl(2;C)-representation of the equation, can construct generators of time dependent symmetries.
Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…
We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the first homology group of compact oriented surfaces.
The Toda hierarchy of size $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ a periodic function, there is a canonical way of defining the initial data for the Toda lattice…
We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is…
The group scheme of ternary automorphisms of a perfect finite dimensional evolution algebra A is computed. The main advantage of using group schemes is that it allows to apply the Lie functor to determine the Lie algebra of ternary…
I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given…
The algebraic and Hamiltonian structures of the multicomponent dispersionless Benney and Toda hierarchies are studied. This is achieved by using a modified set of variables for which there is a symmetry between the basic fields. This…
A box-ball system with more than one kind of balls is obtained by the generalized periodic discrete Toda equation (pd Toda eq.). We study the pd Toda equation in view of algebraic geometry. The time evolution of pd Toda eq. is linearized on…
We discuss a particular stringy modular cosmology with two axion fields in seven space-time dimensions, decomposable as a time and two flat three-spaces. The effective equations of motion for the problem are those of the $SU(3)$ Toda…
This paper establishes three relations between the Toda field theory associated to a simple Lie algebra and the integral curves of the standard differential system on the corresponding complete flag variety. The motivation comes from the…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
New formulations of the solutions of N=1 and N=2 super Toda field theory are introduced, using Hamiltonian Reduction of the N=1 and N=2 super WZNW Models to the super Toda Models. These parameterisations are then used to present the…
The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called {\it evolution loops}). We make a detailed…
It is shown that, in the framework of non-relativistic quantum mechanics, any conserved Hermitian operator (which may depend explicitly on the time) is the generator of a one-parameter group of unitary symmetries of the Hamiltonian and…
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…
The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum…