{'fraction_non_alphanumeric': 0.01870503597122302, 'fraction_numerical': 0.0, 'mean_word_length': 5.5046728971962615, '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}}
CONDITIONAL LIE-BACKLUND SYMMETRY AND REDUCTION OF EVOLUTION EQUATIONS

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to a Lie-Backlund vector field. Such a generalization proves to be effective and enables us to construct principally new ansatz reducing evolution-type equations to several ordinary differential equations. In the framework of the said generalization, we obtain principally new reductions of a number of nonlinear heat conductivity equations ut=uxx+F(u,ux) with poor Lie symmetry and obtain their exact solutions. It is shown that these solutions cannot be constructed by means of the symmetry reduction procedure.