Journal of Nonlinear Mathematical Physics

Volume 11, Issue 3, August 2004

1. A Family of Linearizations of Autonomous Ordinary Differential Equations with Scalar Nonlinearity

Fethi BELKHOUCHE
Pages: 276 - 288
This paper deals with a method for the linearization of nonlinear autonomous diferential equations with a scalar nonlinearity. The method consists of a family of approximations which are time independent, but depend on the initial state. The family of linearizations can be used to approximate the derivative...

2. The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang-Mills System II. The Role of the Centrifugal Term

V I KUVSHINOV, A V KUZMIN, V A PIATROU
Pages: 289 - 293
We have considered SU(2) U(1) gauge field theory describing electroweak interations. We have demonstrated that centrifugal term in model Hamiltonian increases the region of regular dynamics of Yang-Mills and Higgs fields system at low densities of energy. Also we have found analytically the approximate...

3. A Note on Fermionic Flows of the N=(1|1) Supersymmetric Toda Lattice Hierarchy

O LECHTENFELD, A S SORIN
Pages: 294 - 296
We extend the Sato equations of the N=(1|1) supersymmetric Toda lattice hierachy by two new infinite series of fermionic flows and demonstrate that the algebra of the flows of the extended hierarchy is the Borel subalgebra of the N=(2|2) loop superalgebra.

4. A Holomorphic Point of View about Geodesic Completeness

Claudio MENEGHINI
Pages: 297 - 324
We propose to apply the idea of analytical continuation in the complex domain to the problem of geodesic completeness. We shall analyse rather in detail the cases of analytical warped products of real lines, these ones in parallel with their complex counterparts, and of Clifton-Pohl torus, to show that...

5. The Kac Construction of the Centre of U(g) for Lie Superalgebras

Maria GORELIK
Pages: 325 - 349
In 1984, Victor Kac [8] suggested an approach to a description of central elements of a completion of U(g) for any Kac-Moody Lie algebra g. The method is based on a recursive procedure. Each step is reduced to a system of linear equations over a certain subalgebra of meromorphic functions on the Cartan...

6. Replicator - Mutator Evolutionary Dynamics

Vasyl V GAFIYCHUK, Anatoliy K PRYKARPATSKY
Pages: 350 - 360
We consider the general properties of the quasispecies dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system have been studied. Mathematical modeling of the system under consideration has been performed.

7. Superalgebras for the 3D Harmonic Oscillator and Morse Quantum Potentials

H FAKHRI
Pages: 361 - 375
In addition to obtaining supersymmetric structure related to the partner Hamiltonans, we get another supersymmetric structure via factorization method for both the 3D harmonic oscillator and Morse quantum potentials. These two supersymmetries induce also an additional supersymmetric structure involving...

8. Normal Forms for Coupled Takens-Bogdanov Systems

David Mumo MALONZA
Pages: 376 - 398
The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis...

9. Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations

Norbert EULER, Marianna EULER
Pages: 399 - 421
We investigate the Sundman symmetries of second-order and third-order nonlinear odinary differential equations. These symmetries, which are in general nonlocal tranformations, arise from generalised Sundman transformations of autonomous equations. We show that these transformations and symmetries can...