We show that the evolution of the average intensity of cw beams in a quasi-phase-matched quadratic (or ${\chi }^{\left(2\right)}$) medium is strongly influenced by induced Kerr effects, such as self- and cross-phase modulation. We prove the existence of rapidly oscillating solitary waves (a spatial analog of the guided-center soliton) supported by the quadratic and induced cubic nonlinearities.

• Received 18 February 1997

DOI:https://doi.org/10.1103/PhysRevLett.78.4749