Journal of Nonlinear Mathematical Physics

Volume 8, Issue 2, May 2001
Book Review

1. Book Review by P A Clarkson

P.A. Clarkson
Pages: 0 - 0
Peter E Hydon: Symmetry Methods for Differential Equations: A Beginner's Guide Cambridge Texts in Applied Mathematics, Cambridge University Press, 2000.
Research Article

2. Hidden N = (2|2) Supersymmetry of the N = (1|1) Supersymmetric Toda Lattice Hierarchy

O. Lechtenfeld, A. Sorin
Pages: 183 - 195
An N = (2|2) superfield formulation of the N = (1|1) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented.
Research Article

3. Invariants of PL Manifolds from Metrized Simplicial Complexes. Three-Dimensional Case

Igor G. Korepanov
Pages: 196 - 210
An invariant of three-dimensional orientable manifolds is built on the base of a slution of pentagon equation expressed in terms of metric characteristics of Euclidean tetrahedra.
Research Article

4. First Integrals and Parametric Solutions for Equations Integrable Through Lie Symmetries

C. Géronimi, P.G.L. Leach, M.R. Feix
Pages: 211 - 216
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computtion of first integrals gives in the most general...
Short Communication

5. A System of Four ODEs: The Singularity Analysis

S. Yu. Sakovich
Pages: 217 - 219
The singularity analysis is carried out for a system of four first-order quadratic ODEs with a parameter, which was proposed recently by Golubchik and Sokolov. A transfomation of dependent variables is revealed by the analysis, after which the transformed system possesses the Painlevé property and does...
Research Article

6. The Shapovalov Determinant for the Poisson Superalgebras

Pavel Grozman, Dimitry Leites
Pages: 220 - 228
Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C2: these are the Lie superalgebra kL (1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series:...
Research Article

7. Enveloping Superalgebra U(osp(1|2)) and Orthogonal Polynomials in Discrete Indeterminate

A. Sergeev
Pages: 229 - 255
Let A be an associative simple (central) superalgebra over C and L an invariant linear functional on it (trace). Let a at be an antiautomorphism of A such that (at )t = (-1)p(a) a, where p(a) is the parity of a, and let L(at ) = L(a). Then A admits a nondegenerate supersymmetric invariant bilinear form...
Research Article

8. Reflectionless Analytic Difference Operators II. Relations to Soliton Systems

S.N.M. Ruijsenaars
Pages: 256 - 287
This is the second part of a series of papers dealing with an extensive class of anlytic difference operators admitting reflectionless eigenfunctions. In the first part, the pertinent difference operators and their reflectionless eigenfunctions are constructed from given "spectral data", in analogy with...
Research Article

9. Matrix Integrals and the Geometry of Spinors

Johan van de Leur
Pages: 288 - 310
We obtain the collection of symmetric and symplectic matrix integrals and the colletion of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific elements in the Spin-group orbit of the vacuum vector of a fermionic Fock space. This fermionic Fock space is the same...

10. Addendum to: "Coupled KdV Equations of Hirota-Satsuma Type" (J. Nonlin. Math. Phys. Vol. 6, No.3 (1999), 255­262)

S. Yu. Sakovich
Pages: 311 - 312
It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys.,