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• W2026881444 abstract "Mixed superposition rules, i.e., functions describing the general solution of a system of first-order differential equations in terms of a generic family of particular solutions of first-order systems and some constants, are studied. The main achievement is a generalization of the celebrated Lie–Scheffers Theorem, characterizing systems admitting a mixed superposition rule. This somehow unexpected result says that such systems are exactly Lie systems, i.e., they admit a standard superposition rule. This provides a new and powerful tool for finding Lie systems, which is applied here to studying the Riccati hierarchy and to retrieving some known results in a more efficient and simpler way." @default.
• W2026881444 created "2016-06-24" @default.
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• W2026881444 date "2013-01-01" @default.
• W2026881444 modified "2023-09-25" @default.
• W2026881444 title "Mixed superposition rules and the Riccati hierarchy" @default.
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• W2026881444 doi "https://doi.org/10.1016/j.jde.2012.08.020" @default.
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