Journal of Nonlinear Mathematical Physics

Volume 7, Issue 2, May 2000

1. Book Review by B A Kupershmidt

B A Kupershmidt
Pages: 0 - 0
Five books are reviewed, namely Bruce C Berndt: Ramanujan's Notebooks. Part I. (With a foreword by S Chadrasekhar). Springer-Verlag, New York Berlin, 1985. 357 pages. --: Ramanujan's Notebooks. Part II. Springer-Verlag, New York Berlin, 1989. 359 pages. --: Ramanujan's Notebooks. Part III. Springer-Verlag,...

2. Book Reviews by F Calogero

F Calogero
Pages: 0 - 0
Three books are reviewed, namely Masao Nagasawa: Schroedinger Equations and Diffusion Theory. Birkhaeuser, Basel Boston Berlin, 1993. 332 pages. David Wick (with a mathematical appendix by William Farris): The Infamous Bounary - Seven Decades of Controversy in Quantum Physics. Birkhaeuser. Boston...

3. Book Review by P G L Leach

P G L Leach
Pages: 0 - 0
N H Ibragimov: Elementary Lie Group Analysis and Ordinary Differential Equations, John Wiley, New York, 1999, 347 pages.

4. Manin-Olshansky Triples for Lie Superalgebras

Dimitry LEITES, Alexander SHAPOVALOV
Pages: 120 - 125
Following V. Drinfeld and G. Olshansky, we construct Manin triples (g, a, a ) such that g is different from Drinfeld's doubles of a for several series of Lie superalgebras a which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception. Straightforward...

5. First Integrals Generated by Pseudosymmetries in Nambu-Poisson Mechanics

Pages: 126 - 135
Some types of first integrals for Hamiltonian Nambu-Poisson vector fields are obtained by using the notions of pseudosymmetries. In this theory, the homogeneous Hamiltnian vector fields play a special role and we point out this fact. The differential system which describe the SU(2)-monopoles is given...

6. Existence and Homogenization of the Rayleigh-Bénard Problem

Pages: 136 - 169
The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-Bénard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-Bénard experiments with Prandtl number close to one, we prove the existence...

7. Quantized W-algebra of sl(2, 1) and Quantum Parafermions of Uq(^sl(2))

Jintai DING, Boris FEIGIN
Pages: 170 - 183
In this paper, we establish the connection between the quantized W-algebra of sl(2, 1) and quantum parafermions of Uq(^sl(2)) that a shifted product of the two quantum parafermions of Uq(^sl(2)) generates the quantized W-algebra of sl(2, 1).

8. Generalized Operator Yang-Baxter Equations, Integrable ODEs and Nonassociative Algebras

Pages: 184 - 197
Reductions for systems of ODEs integrable via the standard factorization method (the Adler-Kostant-Symes scheme) or the generalized factorization method, developed by the authors earlier, are considered. Relationships between such reductions, operator Yang-Baxter equations, and some kinds of non-associative...

9. Asymptotic Integration of Nonlinear Systems of Differential Equations whose Phase Portrait is Foliated on Invariant Tori

Yuri A. IL'IN
Pages: 198 - 212
We consider the class of autonomous systems x = f(x), where x R2n , f C1 (R2n ) whose phase portrait is a Cartesian product of n two-dimensional centres. We also consider perturbations of this system, namely x = f(x) + g(t, x), where g C1 (R × R2n ) and g is asymptotically small, that is g...

10. Degenerate Poisson Pencils on Curves: New Separability Theory

Pages: 213 - 243
A review of a new separability theory based on degenerated Poisson pencils and the scalled separation curves is presented. This theory can be considered as an alternative to the Sklyanin theory based on Lax representations and the so-called spectral curves.

11. qqq-Newton Binomial: From Euler To Gauss

Pages: 244 - 262
A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter.