Second-order differential invariants of the rotation group O(n) and of   its extensions: E(n), P(1,n), G(1,n)
  Functional bases of second-order differential invariants of the Euclid, Poincar\'e, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant equations. 
W.I. Fushchych, Irina Yehorchenko