Journal of Nonlinear Mathematical Physics

Volume 7, Issue 4, November 2000

1. Book Reviews by F Calogero

F Calogero
Pages: 0 - 0
Four books published by Birkhäuser are reviewed.

2. Dromion Perturbation for the Davey-Stewartson-1 Equations

O.M. KISELEV
Pages: 411 - 422
The perturbation of the dromion of the Davey-Stewartson-1 equation is studied over the large time.

3. A Note on the Appearance of Self-Dual Yang-Mills Fields in Integrable Hierarchies

L. FEHÉR, A. GÁBOR
Pages: 423 - 432
A family of mappings from the solution spaces of certain generalized Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system on R2,2 is described. This provides an extension of the well-known relationship between self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov type.

4. Real Forms of the Complex Twisted N=2 Supersymmetric Toda Chain Hierarchy in Real N=1 and Twisted N=2 Superspaces

O. LECHTENFELD, A. SORIN
Pages: 433 - 444
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demostrated that they possess a global twisted N=2 supersymmetry. We discuss a new superfield basis in which the supersymmetry transformations are...

5. Symmetry, Singularities and Integrability in Complex Dynamics I: The Reduction Problem

P.G.L. LEACH, S COTSAKIS, G.P. FLESSAS
Pages: 445 - 479
Quadratic systems generated using Yang-Baxter equations are integrable in a sense, but we display a deterioration in the possession of the Painlevé property as the number of equations in each `integrable system' increases. Certain intermediate systems are constructed and also tested for the Painlevé...

6. On Symmetries of Chern-Simons and BF Topological Theories

T.A. IVANOVA, A.D. POPOV
Pages: 480 - 494
We describe constructing solutions of the field equations of Chern-Simons and toplogical BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries...

7. Jordan Manifolds and Dispersionless KdV Equations

I.A.B. STRACHAN
Pages: 495 - 510
Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation...

8. Darboux First Integral Conditions and Integrability of the 3D Lotka-Volterra System

Laurent CAIRO
Pages: 511 - 531
We apply the Darboux theory of integrability to polynomial ODE's of dimension 3. Using this theory and computer algebra, we study the existence of first integrals for the 3­dimensional Lotka­Volterra systems with polynomial invariant algebraic solutions linear and quadratic and determine numerous cases...