{'fraction_non_alphanumeric': 0.021235521235521235, 'fraction_numerical': 0.0, 'mean_word_length': 5.253012048192771, '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}}
Lie point symmetries and an approximate solution for the Schrödinger–Newton equations

We consider two problems arising in the study of the Schrödinger–Newton equations. The first is to find their Lie point symmetries. The second, as an application of the first, is to investigate an approximate solution corresponding to widely separated lumps of probability (analogous to the geodesic approximation for BPS monopoles). The lumps are found to move like point particles under a mutual inverse-square law of attraction.