{'fraction_non_alphanumeric': 0.020202020202020204, 'fraction_numerical': 0.0, 'mean_word_length': 5.048780487804878, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the speed of solitary waves running down a vertical wall

Solitary-wave solutions to surface equations or two-equation models of film flows are investigated within the framework of dynamical system theory. The limiting behaviour of one-humped solitary waves (homoclinic orbits) at large Reynolds numbers is considered. Their predicted speed is in good agreement with numerical findings. The theory also explains the absence of solitary-wave solutions to the Benney equation in the same limit.