Internal modes and instabilities of parametric self-trapping in Kerr planar waveguides

Summary form only given. We analyze the structure and stability properties of (1+1)-dimensional higher-order bright spatial solitary waves existing in cubic, weakly anisotropic media under the phase-matched condition when the fundamental wave is coupled to its third harmonic. We have analyzed the structure of higher-order self-trapped beams and bifurcation phenomena due to parametric interactions in optical planar Kerr waveguides. Stability analysis has identified both internal modes and oscillatory instabilities for different soliton branches.