Dynamics of a soliton in a generalized Zakharov system with dissipation

A generalized Zakharov system (describing interaction of dispersive and nondispersive waves in one dimension), with direct self-interaction of the dispersive waves and weak dissipation in the dispersive subsystem, is considered. Evolution of a one-soliton state under the action of weak dissipation is analyzed. It is proved analytically that three different scenarios of evolution are possible: adiabatic (slow) transformation of a moving subsonic soliton into a stable quiescent one, complete adiabatic decay of a transsonic soliton with small amplitude, and the appearance of a transsonic one with a large amplitude into a critical state, from which a further adiabatic evolution is not possible (it corresponds to a local minimum in the dependence of the solitons momentum on its velocity). In the latter case, numerical investigation of the further evolution of the soliton is performed. It is demonstrated that, in a general case, it abruptly splits into a stable quiescent soliton, the slowly decaying small-amplitude transsonic one, and a pair of left- and right-traveling acoustic pulses slowly fading under the action of weak dissipation.