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math-ph2012★ 40 cited
Lie point symmetries of a general class of PDEs: The heat equation
Andronikos Paliathanasis, Michael Tsamparlis
We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form (D/(Ds))(((Dx^{i}(s))/(Ds)))=F(x^{i}(s),x…
math-ph2012★ 20 cited
Generalizing the autonomous Kepler Ermakov system in a Riemannian space
Michael Tsamparlis, Andronikos Paliathanasis
We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov dynamical system to three dimensions using the sl(2,R) invariance of Noether symmetries and determine all th…