366 research outputs found
Graded Lie algebras, representation theory, integrable mappings and systems: nonabelian case
The exactly integrable systems connected with semisimple series for
arbitrary grading are presented in explicit form. Their general solutions are
expressed in terms of the matrix elements of various fundamental
representations of groups. The simplest example of such systems is the
generalized Toda chain with the matrices of arbitrary dimensions in each point
of the lattice.Comment: LaTeX, 19 page
Multi-soliton Solutions of Two-dimensional Matrix Davey-Stewartson Equation
The explicit formulae for m-soliton solutions of (1+2)-dimensional matrix
Davey-Stewartson equation are represented. They are found by means of known
general solution of the matrix Toda chain with the fixed ends [1]. These
solutions are expressed trough m+m independent solutions of a pair of linear
Shrodinger equations with Hermitian potentials.Comment: 13 pages, uses article.st
Integrable Mappings for Non--Commutative Objects
The integrable mappings formalism is generalized on non--commutative case.
Arising hierarchies of integrable systems are invariant with respect to this
"quantum" discrete transformations without any assumption about commutative
properties of unknown operators they include. Partially, in the scope of this
construction are the equations for Heisenberg operators of quantum (integrable)
systems.Comment: 9 page
Discrete transformation for matrix 3-waves problem in three dimensional space
Discrete transformation for 3- waves problem is constructed in explicit form.
Generalization of this system on the matrix case in three dimensional space
together with corresponding discrete transformation is presented also.Comment: LaTeX, 16 page
Light-Cone Parametrizations for K\"Ahler Manifolds
It is shown that, for any K\"ahler manifold, there exist parametrizations
such that the metric takes a block-form identical to the light-cone metric
introduced by Polyakov for two-dimensional gravity. Besides its possible
relevence for various aspects of K\"ahlerian geometry, this fact allows us to
change gauge in W gravities, and explicitly go from the conformal (Toda) gauge
to the light-cone gauge using the W-geometry we proposed earlier (this will be
discussed in detail in a forthcoming article).Comment: (10 pages, no figure, simple LATEX file); preprint LPTENS-93/15,
UT-63
Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy
An infinite class of fermionic flows of the N=(1|1) superconformal Toda
lattice hierarchy is constructed and their algebraic structure is studied. We
completely solve the semi-infinite N=(1|1) Toda lattice and chain hierarchies
and derive their tau functions, which may be relevant for building
supersymmetric matrix models. Their bosonic limit is also discussed.Comment: 11 pages, no figures, revised version published in Nucl. Phys.
Gauge Conditions for the Constrained-WZNW--Toda Reductions
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
decompositions in relevent gauges, we unify formulae already derived, and
explictly determine the holomorphic expansion of the conformally reduced WZNW
solutions - whose restriction gives the solutions of the Toda equations. The
same takes place also for semi-integral gradations. Most of our conclusions are
also applicable to the affine Toda theories.Comment: 12 pages, no figure
The Solution of the N=2 Supersymmetric f-Toda Chain with Fixed Ends
The integrability of the recently introduced N=2 supersymmetric f-Toda chain,
under appropriate boundary conditions, is proven. The recurrent formulae for
its general solutions are derived. As an example, the solution for the simplest
case of boundary conditions is presented in explicit form.Comment: 15 pages, latex, no figure
UV manifold and integrable systems in spaces of arbitrary dimension
The dimensional manifold with two mutually commutative operators of
differentiation is introduced. Nontrivial multidimensional integrable systems
connected with arbitrary graded (semisimple) algebras are constructed. The
general solution of them is presented in explicit form
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