We perform a linear stability analysis of stationary periodic waves in cubic–quintic nonlinear media and show that weak χ<sup>(5)</sup> nonlinearity can lead to stabilization of cnoidal and destabilization of snoidal periodic wave patterns existing in focusing and defocusing χ<sup>(3)</sup> 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
Yaroslav V. Kartashov, Victor A. Vysloukh, Alexey A. Egorov, and Anna S. Zelenina, "Stable periodic waves supported by competing cubic-quintic nonlinearity," J. Opt. Soc. Am. B 21, 982-988 (2004)