The structure of the fundamental matrix of a system of coupled-mode equations

In the paper, a system of coupled-mode equations is considered which is a mathematical model for a waveguide. We deal with problems alike those treated by R. F. Matveev, M. H. Zahar-Itkin and G. C. Papanicolaou, but in the present paper we investigate the structure of the fundamental matrix in the whole, while the above-mentioned authors studied it partly. We use the «orispherical» coordinates. For the diagonal component of the fundamental matrix a theorem analogous to the strong law of large numbers is obtained.