| Abstract: | This paper presents analytical and numerical solutions of a new amplitude equation governing long waves on thin films. At lowest order in the long-wave parameter, the equation is nondispersive and represents a balance between nonlinearity and cross-stream diffusion. Numerical solutions tracing the temporal evolution of an initially localized disturbance indicate that the aforementioned diffusion partly mitigates the tendency of the wave to break. We have also obtained a closed-form solution resembling an undular bore propagating in an oblique direction. |
