We study the geometry of differential equations determined uniquely by their point symmetries, that we call 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–Ampère equations in two independent variables of various orders.
Manno, G., Oliveri, F., Vitolo, R. (2007). On differential equations characterized by their Lie point symmetries. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 332(2), 767-786 [10.1016/j.jmaa.2006.10.042].
On differential equations characterized by their Lie point symmetries
MANNO, GIOVANNI;
2007
Abstract
We study the geometry of differential equations determined uniquely by their point symmetries, that we call 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–Ampère equations in two independent variables of various orders.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
