Periodical waves, domain walls, and modulational instability in dispersive quadratic nonlinear media

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Abstract
We show that the three-wave mixing interaction in media with quadratic nonlinearity, and dispersion up to the second order, possess classes of mutually sustained periodical nonlinear traveling waves and domain walls (or kink pairs). We also predict a particular kind of Benjamin-Feir, or modulational instability. This mechanism may also affect the stability of certain classes of localized waves. These phenomena have importance in different branches of physics whenever parametric interactions may occur through quadratic nonlinearities.