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The Kuramoto-Sivashinsky (KS) equation is derived as a phase equation using the perturbative renormalization group method. In our derivation, it is not necessary to introduce an unusual small scale for the phase, which is crucial in deriving the KS equation by means of standard methods, such as the reductive perturbation method. The higher order KS equation is also derived consistently.

Derivation of the Kuramoto-Sivashinsky Equation Using the Renormalization Group Method