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...
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...
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...
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.
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
M). When M is the n-dimensional sphere, Sn
, we use this
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.
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...
In a previous paper the real evolution of the system of ODEs
¨zn + zn =
gnm(zn - zm)
zn zn(t), zn
, 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...
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....
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...