A GENERALIZED SIDE-BAND STABILITY THEORY VIA CENTER MANIFOLD PROJECTION

A center manifold theory is used to determine all modes that contribute significantly to the leading-order sideband stability of finite-amplitude monochromatic waves. The classical multiscale theories based on the Ginzburg-Landau equation are extended away from near-critical conditions and are shown to have omitted an important contribution from nonlinear interactions with low wave-number modes. Stability bounds on stable monochromatic waves are reported for dispersive systems that extend the classical Eckhaus bound for nondispersive systems and the Lange-Newell and Benjamin-Feir stability conditions for monochromatic waves with critical wave numbers. These new stability bounds are verified numerically by computing the evolving spectrum of a model equation. © 1990 American Institute of Physics.