Possible nonlinear wave-wave coupling between three or four waves in plasmas

Since even weak nonlinear coupling between coherent waves can change the stability or instability of these waves, as computed from linearized theory, more and more cases of such wave-wave coupling are investigated. From a theoretical point of view, however, far more cases of nonlinear wave-wave coupling are possible than can be generally be surmised from papers available on this subject. The reason lies in the fact that certain combinations of resonance conditions give rise to a totally different situation, as far as the equations governing the changes in the interacting amplitudes are concerned. This constatation remains valid even when one set of resonance conditions is a special case of another one. Hence it becomes necessary to look for all the different resonance conditions which yield distinct sets of amplitude equations and thus different solutions. This has been done for coupling between two, three or four waves, in second or in third order. The remaining question is then whether some of these new resonance conditions can be traced or realized in existing or possible experimental conditions. If a wave can coexist and interact with certain of its harmonics, some of the newly found wave-wave coupling cases might indeed occur and even dominate, possibly in the ionosphere. To investigate this requires subsequent calculations on perhaps a more detailed model. (author)