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Many methods for reducing and simplifying differential equations are known.They provide various generalizations of the original symmetry approach ofSophus Lie. Plenty of relations between them have been noticed and in this notea unifying approach will be discussed. It is rather close to the classicaldifferential constraint method, but we provide certain rigorous results basingon recent advances in compatibility theory of non-linear overdetermined systemsand homological methods for PDEs.

Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method