Collisions of three-wave solitons in media with competing quadratic and cubic nonlinearities

We report results of analysis of collisions between in-phase spatial solitons in a three-wave system, which includes competing χ⁽²⁾:χ⁽³⁾ nonlinearities and birefringence. The character of the collisions is quantified by a critical value of the initial tilt of the colliding solitons, Q, which separates quasielastic passage and merger (solitons with phase shift π bounce from each other). If Q is very close to Qcr, the solitons may fuse into a double-peak state. Qcr is smaller for relatively large negative mismatch of the χ⁽²⁾ interactions. With the increase of the χ⁽³⁾/χ⁽²⁾ ratio, the system quickly transits from the behavior governed by the χ⁽²⁾ nonlinearity to a regime dominated by the χ⁽³⁾ terms.