We consider the one-dimensional porous medium equation ut = (un
ux)x + µ
derive point transformations of a general class that map this equation into itself or into
equations of a similar class. In some cases this porous medium equation is connected
with well known equations. With the...
In this paper we consider the Poisson algebraic structure associated with a classical
r-matrix, i.e. with a solution of the modified classical YangBaxter equation. In Section 1 we recall the concept and basic facts of the r-matrix type Poisson orbits. Then
we describe the r-matrix Poisson pencil (i.e...
A symplectic theory approach is devised for solving the problem of algebraic-analytical
construction of integral submanifold imbeddings for integrable (via the nonabelian
Liouville-Arnold theorem) Hamiltonian systems on canonically symplectic phase spaces.
We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the r-matrix framework. An r-matrix account of the nonrelativistic lattice
KP hierarchy is also provided for the reader's convenience. All relativistic constructions are regular one-parameter perturbations...
The notion of classical r-matrix is re-examined, and a definition suitable to differential
(-difference) Lie algebras, where the standard definitions are shown to be deficient,
is proposed, the notion of an O-operator. This notion has all the natural properties
one would expect form it, but lacks...