We report the existence of whole families of stationary cnoidal, periodic wave patterns in quadratic nonlinear media. We study the main physical features of the multicolored light patterns, including their shape, contrast, multifrequency energy sharing, asymptotics in the cascading limit, and excitation. Our numerical simulations predict that the cnoidal waves with high and even with moderate contrasts are robust enough against modulational instabilities to be experimentally observable.
Kartashov, Y.V., Vysloukh, V.A., Torner, L. Cnoidal wave patterns in quadratic nonlinear media. "Physical review E, statistical physics, plasmas, fluids, and related interdisciplinary topics", Juliol 2003, vol. 67, p. 66612-66617.