An integro-differential formulation for the equation governing the Alfven waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time-dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfven wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing. (author). 8 refs.