Soliton resonance in ion beam plasma

The equations to describe the non-linear wave phenomena of plasma in which ion beam exists were derived. Three kinds of soliton modes were deduced as the steady solutions of the equations, and the resonance conditions between solitons were satisfied. The equations were derived by the long wavelength approximation. The equations were two-dimensional equations, and have become Kadomtseuv-Petviashvilli equations including beam effect. The linear stability of the equations was studied, and it was found that the system sometimes became unstable in the long wavelength region. The steady soliton solution was investigated. There are resonance conditions among three linear modes. It is possible to make similar conditions among three soliton modes. (Kato, T.)