SELF-FOCUSING AND SOLITON-LIKE STRUCTURES IN MATERIALS WITH COMPETINGQUADRATIC AND CUBIC NONLINEARITIES

We study the mutual influence of quadratic and cubic nonlinearities on the propagation of the coupled fundamental and second harmonic waves in asymmetric optical media. For attractive potentials with positive c oupling parameters, it is shown that, in systems with two and three tr ansverse dimensions, mutually trapped waves can self-focus until colla pse whenever their respective powers exceed some thresholds. On the co ntrary, coupled waves diffracting in a one-dimensional plane never col lapse and may evolve towards stable solitonlike structures. For higher transverse dimension numbers, we investigate the question of forming two-component solitons and determine criteria for their stability.