A WKB-derived reduced wave-number equation captures unstable states, self-similar singularities, and traveling shocks in the real and complex Ginzburg-Landau equations, with exact profiles and DNS agreement in the nearly-real limit.
Whenk 0 >1/ √ 3, the coefficient D0 <0, leading to antidiffusion as in the KS equation
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Reduced wave number dynamics in the real and complex Ginzburg-Landau equations
A WKB-derived reduced wave-number equation captures unstable states, self-similar singularities, and traveling shocks in the real and complex Ginzburg-Landau equations, with exact profiles and DNS agreement in the nearly-real limit.