Soliton generation in the nonlinear interaction of two waves

We consider interaction of a laser field with surface waves propagating in a thin layer having a width much less than that of the laser field. It is assumed that the laser field interacts concurrently with a two-level transition. We show that generation of the surface waves in this scheme may be described by the completely integrable Thirring model. We use this model for study of the evolution of a steplike pulse. It is found that a leading edge is described asymptotically by a sequence of solitons. The modulation instability leading to the formation of these solitons is treated in a hydrodynamic approximation. For this aim we find a solution to the Whitham equations associated with deformation of the one-phase solution of the Thirring model. We show that the results obtained here can be applied to other physical situations, for instance, the study of the three-wave mixing in a bulk medium.