21 research outputs found
On existence of an x-integral for a semi-discrete chain of hyperbolic type
A class of semi-discrete chains of the form is
considered. For the given chains easily verifiable conditions for existence of
x-integral of minimal order 4 are obtained
Semi-discrete hyperbolic equations admitting five dimensional characteristic -ring
The necessary and sufficient conditions for a hyperbolic semi-discrete
equation to have five dimensional characteristic {\it x}-ring are derived. For
any given chain, the derived conditions are easily verifiable by
straightforward calculations
On a transformation between hierarchies of integrable equations
A transforation between a hierarchy of integrable equations arising from the
standard -matrix construction on the algebra of differential operators and a
hierarchy of integrable equations arising from a deformation of the standard
-matrix is given.Comment: 8 page
On construction of Darboux integrable discrete equations
The problem of discretization of Darboux integrable equations is considered.
Given a Darboux integrable continuous equation, one can obtain a Darboux
integrable differential-discrete equation, using the integrals of the
continuous equation. In the present paper, the discretization of the
differential-discrete equations is done using the corresponding characteristic
algebras. New examples of integrable discrete equations are obtained
On the discretization of Darboux Integrable Systems
We study the discretization of Darboux integrable systems. The discretization
is done using -, -integrals of the considered continuous systems. New
examples of semi-discrete Darboux integrable systems are obtained
Cartan matrices and integrable lattice Toda field equations
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 , , , the
complete sets of integrals in both directions are found. For the simple Lie
algebras of the classical series , , and affine algebras of
series the corresponding systems are supplied with the Lax
representation.Comment: 21 page
Integrable nonlinear equations on a circle
The concept of integrable boundary value problems for soliton equations on
and is extended to bounded regions enclosed by
smooth curves. Classes of integrable boundary conditions on a circle for the
Toda lattice and its reductions are found.Comment: 23 page