Integrable ponderomotive system: Cavitons are solitons

A new set of integrable soliton equations describe caviton formation in a plasma. The equations are solvable by the inverse scattering transform. The time evolution of the scattering data is obtained and it is found that, unlike other integrable equations where the magnitude of the reflection coefficient was always a constant of the motion, here it may grow and/or decay in time. One physical manifestation of the growth of the reflection coefficient is the growth of density ripples in front of a microwave source. On the other hand, when the decay conditions dominate, one is left with only cavitons, which are the solitons for these equations.