Three-Wave Resonant Interactions in Self-Defoucsing OpticalMedia

A three-wave resonant interaction for nonlinear excitations created from a continuous-wave background is shown to be possible in a isotropic optical medium with a self-defocusing cubic nonlinearity. Under suitable phase-matching conditions the nonlinear envelope equations for the resonant interaction are derived by using a method of multiple-scales. Some explicit three-wave solitary wave and lump solutions are discussed.