We study the geometry of differential equations determined uniquely by their point symmetries, that we call \emph{Lie remarkable}. We determine necessary and sufficient conditions for a differential equation to be Lie remarkable. Furthermore, we see how, in some cases, Lie remarkability is related to the existence of invariant solutions. We apply our results to minimal submanifold equations and to Monge-Amp\`ere equations in two independent variables of various orders.
On differential equations determined by the group of point symmetries
MANNO, GIOVANNI;VITOLO, Raffaele
2007-01-01
Abstract
We study the geometry of differential equations determined uniquely by their point symmetries, that we call \emph{Lie remarkable}. We determine necessary and sufficient conditions for a differential equation to be Lie remarkable. Furthermore, we see how, in some cases, Lie remarkability is related to the existence of invariant solutions. We apply our results to minimal submanifold equations and to Monge-Amp\`ere equations in two independent variables of various orders.File in questo prodotto:
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