Journal of Nonlinear Mathematical Physics

Volume 6, Issue 4, November 1995

1. Continuous and Discrete Transformations of a One-Dimensional Porous Medium Equation

Christodoulos SOPHOCLEOUS
Pages: 355 - 364
We consider the one-dimensional porous medium equation ut = (un ux)x + µ x un ux. We 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...

2. Poisson Homology of r-Matrix Type Orbits I: Example of Computation

Alexei KOTOV
Pages: 365 - 383
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...

3. The Nonabelian Liouville-Arnold Integrability by Quadratures Problem: a Symplectic Approach

Anatoliy K. PRYKARPATSKY
Pages: 384 - 410
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.

4. r-Matrices for Relativistic Deformations of Integrable Systems

Yuri B. SURIS
Pages: 411 - 447
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...

5. What a Classical r-Matrix Really Is

Boris A. KUPERSHMIDT
Pages: 448 - 488
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...