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We study nonlinear propagation of surface plasmon polaritons along an interface between metal and nonlinear Kerr dielectric. We demonstrate numerically self-focusing of a plasmon beam at large powers and the formation of slowly decaying spatial soliton in the presence of losses. We develop an analytical model for describing the evolution of spatial plasmon-solitons and observe a good agreement with numerical results.

We analyze phase matching in metal-dielectric nonlinear structures which support highly localized plasmon polariton modes. We reveal that quadratic phase matching between the plasmon modes of different symmetries becomes possible in planar waveguide geometries. We discuss the example of a nonlinear LiNbO(3) waveguide sandwiched between two silver plates, and demonstrate that second-harmonic generation can be achieved for interacting plasmonic modes.