Beta-approximation of the two-particle distribution function for the chains of phase oscillators

Abstract: When constructing the BBGKY hierarchy for systems with strong local interaction (liquids, magnetic materials) the key problem is the issue of approximation of the two-particle distribution function. The traditional approximation of multiplicativity that leads to the theory of the mean field often gives qualitatively incorrect results. In this paper, we consider a ring chain of phase oscillators with interaction only between the nearest neighbors, in a thermostat. On the basis of the analysis of the results of ab initio calculations, an approximation is constructed for the two-particle distribution function. It results in the one-particle Fokker-Planck equation with a self-consistent integral force. The results of the modeling based on the resulting equation are in a good agreement with the ab initio calculations. The obtained results may be of great importance in the construction of self-consistent models of systems with strong local interaction and temperature fluctuations.Note: Research direction:Mathematical modelling in actual problems of science and technic