Soliton phenomena in unstable media

As a canonical equation for soliton phenomena in unstable media, the unstable nonlinear Schrodinger (UNS) equation, i q x + q tt +2| q | 2 q =0 is proposed. The UNS equation is derived for two physical systems, Rayleigh-Taylor instability and electron beam plasma. It is shown that the initial value problem can be solved by the inverse scattering method. The exact N -soliton solution gives information on the soliton interaction: the faster (slower) soliton has negative (positive) position shift. It is thus concluded that soliton interaction in unstable media is attractive. Further, it is reported that the UNS equation explains a recent observation on propagations of localized structures in electron beam plasma.