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Stable periodic waves supported by competing cubic–quintic nonlinearity

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Abstract

We perform a linear stability analysis of stationary periodic waves in cubic–quintic nonlinear media and show that weak χ(5) nonlinearity can lead to stabilization of cnoidal and destabilization of snoidal periodic wave patterns existing in focusing and defocusing χ(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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