My main subject of interest is nonlinear wave dynamics in chemical systems.

The famous example of such a system is the Belousov-Zhabotinsky (BZ) reaction. If the reagents are poured into a Petri dish, one can observe propagating chemical waves. These waves are emitted by unusual wave-sources - by SPIRAL WAVES.

The dynamics of spiral waves has been investigated in good detail. I participated in the projects to investigate the dependence of characteristics of spiral waves on reagent concentrations and the temperature [5] (here and below the numbers in square brackets are the references in my reference list).

It was also found that under electric field with symmetry group SO(2) [6], the spiral wave changes its shape and become a super-spiral [4]. In the inhomogeneous medium with symmetry R(1) there is a drift of spiral wave [5].

To investigate the dynamics of 3D vortices there was developed a stable procedure of shaping all the basic vortices: simple vortex, vortex ring, twisted vortex. Twisted vortex was observed experimentally for the first time [2]. The dynamics of vortex rings with noncircular filament was investigated both analytically and experimentally in the ref. [1].

From physics it is known that there are two types of waves: trigger-waves and phase-waves. It is interesting that the BZ reaction maintains both this types of waves. Moreover, these waves can transform to each other [11]. Such a transformation, as well as the dynamics of phase-waves plays an important role while using the BZ reaction as an image-processor.

Another interesting application of the BZ reaction is the use of this reaction to simulate more sophisticated systems, such as the heart [13]. See the use of the BZ reaction to study Vulnerability (well-known problem for cardiologists) in refs.[8,9,13,15].

In the most part of cases it is impossible to solve analytically nonlinear systems. Some of interesting approaches to this can be found in refs.[1,7]. One of possible routes to chaos in a nonlinear system is presented in ref.[14].