Dirac-Lie systems and Schwarzian equations
In this interesting work, the authors develop a new type of Lie systems on Dirac manifolds that enlarges the notion of Lie-Hamilton systems. Their main geometrical features are analyzed in detail, and their potential use in the analysis of different systems like the SKdV is shown. The main interest, however, is the possibility of studying systems that are not covered by the usual techniques. In particular, criteria for bi-Dirac systems are developed, allowing to deduce the constants of the motion and superposition rules, among other properties. Prospective generalizations of the method to cover other types of systems are discussed.
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