= Large solitary pulse on a cylindrical film
{title2=$H_{\max}\sim2\kappa(3c)^{2/3}$}
For a <travelling wave> of large positive speed in the cylindrical film equation, the leading core is proportional to $1-\cos x$ over an axial interval of length $2\pi$. Edge coordinates $X=(3c)^{1/3}(x-x_e)$ reduce the transition equation to $H^3H_{XXX}=H-1$. Its real positive exponent gives a monotone trailing approach and its complex stable exponents give damped <capillary waves> ahead, with physical wavelength $4\pi a/(3^{5/6}c^{1/3})$. Matching the two quadratic edge expansions selects the uniform film thickness; this is a <matched asymptotic expansion>, valid while the pulse itself remains thin relative to the cylinder.
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