Lie families: theory and applications

Details Lie families: theory and applications Lie families: theory and applications

2010-03-18

arxiv.org/abs/1003.3529v3

J. Phys. A: Math. Theor. 43, 305201 (2010)

Mathematics

Classical Analysis and ODEs

23 pages, revised version to appear in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/43/30/305201

We analyze families of non-autonomous systems of first-order ordinary differential equations admitting a common time-dependent superposition rule, i.e., a time-dependent map expressing any solution of each of these systems in terms of a generic set of particular solutions of the system and some constants. We next study relations of these families, called Lie families, with the theory of Lie and quasi-Lie systems and apply our theory to provide common time-dependent superposition rules for certain Lie families.

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