The new mathematical results are presented, which open a possibility of solving the wide class of microcosm problems at the scales of the atom distances and times. The new approach allows detailed quantitative study of the nuclear reactions dynamics and control this processes with the aim to increase the power of energy release. The analysis of the fundamentals of the mathematical theory of physical vacuum (ether) is given, based on a comparison with the Newton’s second law and classical equations of continuum mechanics. The mathematical problems are formulated, describing the dynamics of the hydrogen mesoatom formation from proton and muon. The problem of controlling this process is considered. A brief description of the algorithm for numerical solution of the problem of the ether dynamics is given and its application is illustrated.

Keywords: equations in partial derivatives, mathematical models, complex dynamic systems, control, numerical modeling, physical vacuum (ether).