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.

We theoretically investigate the properties of phonon-polariton inhomogeneous harmonic wave, cnoidal wave and spatial soliton propagating in boundless dielectric medium and compute the shape of nonlinear vector polariton wave. We obtain analytically the envelopes of linearly polarized nonlinear polariton waves in the self-focusing and self-defocusing media.

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We obtain theoretically the phonon-polariton spectrum in nonlinear dielectric medium with the third order Kerr-type nonlinearity. We investigate the dependence of number of the polariton spectrum branches on the intensity of electromagnetic field and demonstrate that the appearance of new branches located in the polariton spectrum gap is caused by the influence of dispersion of the third order dielectric susceptibility at intensity field in the medium. The modulation instability of new branch waves leading to appearance of cnoidal waves and solitons.

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