Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Abstract: We say that a system of first-order differential equations admits a superposition principle if its general solution can be written somehow in terms of a finite set of particular solutions and a set of constants. Differential equations admiting this property were characterized by S. Lie. Nevertheless, this characterization has some practical problems. In this talk, we investigate superposition principles from the point of view of the modern differential geometry and we analyze some of the practical problems of Lie's characterization.