Traveling waves on fluid interfaces: Normal form analysis of the Kuramoto–Sivashinsky equation

Traveling wave solutions of the Kuramoto–Sivashinsky equation, hθ+4hhη+hηη+shηηηη=0, are investigated using the normal form analysis of nonlinear dynamic theory. Theoretical correlations between wavelength and amplitude and between wave velocity and amplitude are obtained for periodic and solitary propagating patterns. Since the equation describes several interfacial instabilities, these correlations are relevant to many physical phenomena. They are favorably compared to experimental data of finite waves on vertically falling films.

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