Journal of Nonlinear Mathematical Physics

Volume 9, Issue 4, November 2002
Research Article

1. The Influence of Quantum Field Fluctuations on Chaotic Dynamics of Yang­Mills System

V.I. Kuvshinov, A.V. Kuzmin
Pages: 382 - 388
On example of the model field system we demonstrate that quantum fluctuations of non-abelian gauge fields leading to radiative corrections to Higgs potential and spontaneous symmetry breaking can generate order region in phase space of inherently chaotic classical field system. We demonstrate on the...
Research Article

2. The Scattering Approach for the Camassa—­Holm equation

Jonatan Lenells
Pages: 389 - 393
We present an approach proving the integrability of the Camassa­—Holm equation for initial data of small amplitude.
Research Article

3. On Einstein Equations on Manifolds and Supermanifolds

D. Leites, E. Poletaeva, V. Serganova
Pages: 394 - 425
The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactifcation M becomes the Grassmannian Gr4 2 of 2-dimensional subspaces in the 4-dimesional complex one. Here we answer for which of the classical...
Research Article

4. The Incompressible Navier­Stokes for the Nonlinear Discrete Velocity Models

A. Bellouquid
Pages: 426 - 445
We establish the incompressible Navier­Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which rmain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled families solutions of discrete Boltzmann equation...
Research Article

5. On a One-Phase Stefan Problem in Nonlinear Conduction

S. De Lillo, M.C. Salvatori
Pages: 446 - 454
A one phase Stefan problem in nonlinear conduction is considered. The problem is shown to admit a unique solution for small times. An exact solution is obtained which is a travelling front moving with constant speed.
Research Article

6. Cohomology of Groups of Diffeomorphisms Related to the Modules of Differential Operators on a Smooth Manifold

Sofiane Bouarroudj
Pages: 455 - 463
Let M be a manifold and T M be the cotangent bundle. We introduce a 1-cocycle on the group of diffeomorphisms of M with values in the space of linear differential operators acting on C (T M). When M is the n-dimensional sphere, Sn , we use this
Research Article

7. The Landau­Ginzberg Theory for the Two-Dimensional Bose Gas

Harry L. Morrison, Achilles D. Speliotopoulos
Pages: 464 - 474
Using results from sheaf theory combined with the phenomenological theory of the two-dimensional superfluid, the precipitation of quantum vortices is shown to be the genesis of a macroscopic order parameter for a phase transition in two dimensions.
Research Article

8. On the Lie Symmetries of Kepler­Ermakov Systems

Ayse Karasu (Kalkanli), Hasan Yildirim
Pages: 475 - 482
In this work, we study the Lie-point symmetries of Kepler­Ermakov systems presented by C Athorne in J. Phys. A24 (1991), L1385­L1389. We determine the forms of arbitrary function H(x, y) in order to find the members of this class possessing the sl(2, R) symmetry and a Lagrangian. We show that these systems...
Research Article

9. Periodic Solutions of a System of Complex ODEs. II. Higher Periods

F. Calogero, M. Sommacal
Pages: 483 - 516
In a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers,...
Research Article

10. Tau Functions Associated to Pseudodifferential Operators of Several Variables

Min Ho Lee
Pages: 517 - 529
Pseudodifferential operators of several variables are formal Laurent series in the formal inverses of 1, . . . , n with i = d/dxi for 1 i n. As in the single variable case, Lax equations can be constructed using such pseudodifferential operators, whose solutions can be provided by Baker functions. We...
Research Article

11. On the Bilinear Equations for Fredholm Determinants Appearing in Random Matrices

J. Harnad
Pages: 530 - 550
It is shown how the bilinear differential equations satisfied by Fredholm determinants of integral operators appearing as spectral distribution functions for random matrices may be deduced from the associated systems of nonautonomous Hamiltonian equations satisfied by auxiliary canonical phase space...