Instability of periodic stationary waves in an active nonlinear medium with high-frequency losses

The stability of stationary waves in nondispersive nonlinear active media with high-frequency losses is studied. It is shown that waves with wavelength greater than some minimum value λ_min can exist in such a medium. All stationary waves are unstable with respect to small perturbations of their profile, but as the wavelength increases, the lifetime of the wave increases and for waves with long wavelengths λ the lifetime can be long enough that these waves can in some sense be regarded as stable. Pis’ma Zh. Tekh. Fiz. 24, 80–87 (January 26, 1998)