TIME EVOLUTION OF ALFVEN-TURBULENCE SPECTRA IN A COLLISIONLESS PLASMA

With allowance for induced scattering and two-wave absorption, a study is conducted of the properties of solutions to time-dependent nonline ar equations describing the time evolution of Alfven-turbulence spectr a in a collisionless plasma with the parameter beta less than or simil ar to 1. It is shown that the integral form of the operator describing the interaction must be retained because, in the opposite case, the s olution becomes multivalued and wavebreaking occurs. In the presence o f a ''turbulent source'' which is localized in a narrow frequency rang e omega approximate to omega(s), the nonstationary spectrum W(omega, t ) oscillating with respect to the stationary solution W(omega) proport ional to 1/omega arises in the range omega less than or similar to ome ga(s). In all cases, when beta much less than 1, the energy is transfe rred to and accumulated in the region omega --> 0. This gives rise to the modulational instability of Alfven waves.