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.
(20)–(22) that is a smooth heteroclinic orbit with tails connecting two distinct wave numbersk 1 ̸=k 2 atξ→ ±∞and hence no such solution of Eq
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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.