Abstract

We perform a linear stability analysis of stationary periodic waves in cubic–quintic nonlinear media and show that weak ${\chi }^{(5)}$ nonlinearity can lead to stabilization of cnoidal and destabilization of snoidal periodic wave patterns existing in focusing and defocusing ${\chi }^{(3)}$ media, respectively. Direct computer simulations confirm results of the linear stability analysis. The stabilization of periodic waves is expected to be a common phenomenon in physical systems where focusing–defocusing, attractive–repulsive, nonlinear self-actions compete with each other.

© 2004 Optical Society of America

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