Large solitary pulse on a cylindrical film ($H_{\max }\sim 2\kappa (3c{)}^{2/3}$)

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 $H^3{H}_{XXX}=H-1$. 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.