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...
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...
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
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...
In 1984, Victor Kac  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...
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.
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...
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...
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...