Waves in the Skyrme--Faddeev model and integrable reductions

In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation of periodic wave states, leading to a quasi-linear system. The reduction to general hydrodynamic systems have been considered and it is compared with other integrable reductions of the system.Comment: 16 pages, 5 figure

Studying the system of pipe header telemechanics on the basis of communication network of GSM standard

Studying the system of pipe header telemechanics on the basis of communication network of GSM standard has been covered, the results of experiments for two services of GSM have been given. The way of increasing system response speed is suggested and GSM is compared with other services applied at the present in pipe header telemechanics system

A normal form for excitable media

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao

Wave Instabilities in Excitable Media with Fast Inhibitor Diffusion

An excitable activator-inhibitor system with relatively fast inhibitor diffusion is considered. Numerical simulations of wave propagation inside long channels show transitions from stable flat traveling waves to folded waves and further to spreading spiral turbulence as the inhibitor diffusivity is increased. For sufficiently narrow channels the suppression of turbulence and the development of regular steadily propagating patterns is observed. The curvature dependence of the wave propagation velocity is derived and used to interpret the observed phenomena

Controlling Spiral Waves in Confined Geometries by Global Feedback

The evolution of spiral waves on a circular domain and on a spherical surface is studied by numerical integration of a reaction-diffusion system with a global feedback. It is shown that depending on intensity, sign, and/or time delay in the feedback loop a global coupling can be effectively used either to stabilize the rigid rotation of a spiral wave or to completely destroy spiral waves and to suppress self-sustained activity in a confined domain of an excitable medium. An explanation of the numerically observed effects is produced by a kinematical model of spiral wave propagation