Summary form only given. Quadratic solitons, that form through cascading in materials with second-order nonlinearities, are a topic of current intense investigation. Solitons have been observed in second harmonic generation (SHG) and in parametric amplification schemes, and many of their basic properties are well established. In particular, families of spatial and temporal solitons existing in waveguides and in bulk geometries are known, including those existing in settings with a small Poynting vector walk-off and/or temporal group-velocity mismatch. Under conditions where modulational instabilities can not grow, such families of solitons are stable under propagation and robust against several perturbations.

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