Recently the great interest is aimed on the phenomena near threshold, such as phase transitions, turbulence, fractals, selforganised systems, etc. Since these systems are sensitive to the external actions there are the experimental problems in their investigations. Therefore in this case are widely used the methods with minimal external action. Among them the studying of the parameters of waves transiting through the medium is widely employed. It may be sound and electromagnetic waves. The considered problems are of interest in physics and mathematics simultaneous. Recently the serious attention is paid on the propagation and scattering of waves in highly inhomogeneous media. This problem appears in the various spheres of the human activity. In physics it concerns with the studying of the phase transitions, liquid crystals, high temperature superconductors, dust crystals in plasma, studying the systems at high temperature and pressure. In medicine this problem appeared due to importance of transition from X-ray to visible light diagnostics. In geophysics there is the problem of the search of useful minerals analysing the characteristics of the seismic waves.In the physics of atmosphere and ocean and astrophysics this problem exists since the getting of information requires the studying of the waves transiting a very large distance and containing a serious deviations. In these problems it is necessary to extract an information analysing the multiple scattered waves where this information is contained in a very complicate form. Similar problems require using both analytical and numerical calculations including computer simulations.

The unique speciality of liquid crystals is the combination of liquid and crystal properties. These liquids contain the molecular orientation and are optically anisotropic media. At the same time these systems are very sensitive to external fields. In particular the small electric and magnetic fields vary the system orientation and its optical properties. At the same time liquid crystals are sensitive to variation of temperature. They are widely used in the system of mapping including TV and PC monitors. Moreover their capability to very their color with the small temperature variation is widely used in the medicine diagnostics and in microchem technology for analysing the regions where temperature is higher.