About one nonlinear dynamic system arising in a two-phase medium.

The Cauchy problem for a one-dimensional homogeneous system of Hopf-type equations arising in a two-fluid medium is considered. It is believed that energy dissipation occurs only due to the coefficient of friction (D'arcy's analogue) and the Cauchy data are given as a finite Fourier series. Recurrent systems of ordinary differential equations for amplitudes for N approximations are obtained. A partial solution of the resulting Ordinary Differential Equation is constructed for N=3. [ABSTRACT FROM AUTHOR]