Problem of Breakdown of Solitary Waves and Discontinuities

The evolution of initial data of the solitary-wave type with time is investigated numerically. The solitary wave amplitude decreases due to the generation of short-wave radiation. This solution is interpreted as the solution with a discontinuity qualitatively analogous to the solution of the problem of the breakdown of an arbitrary discontinuity in dissipationless systems. The solitary wave amplitude reduction rate is estimated, first for a generalized Korteweg-de Vries equation and then for plasma waves. Features of the investigation are analyzed for cold and hot-electron plasmas.