Transformation of the surface plasmon-polariton pulse to bright and dark solitons at the first and second harmonics

We consider the linear and nonlinear models of generation of the surface plasmon-polaritons on the boundary of a nonmagnetic dielectric medium and a nonmagnetic metal. We show how the three-dimensional incident wave is transformed to fluxes of surface plasmon-polaritons at the first and second harmonics of the transverse magnetic mode. These 'slow' and 'fast' fluxes of the surface plasmon-polaritons are formed at the first and second harmonics when their interaction is weak. We demonstrate that an input surface plasmon-polariton pulse transforms to bright and dark solitons for a strong harmonic interaction.