F. Gungor, NONLINEAR EQUATIONS INVARIANT UNDER POINCARE, SIMILITUDE AND CONFORMAL-GROUP IN 3-DIMENSIONAL SPACETIME, Journal of physics. A, mathematical and general, 31(2), 1998, pp. 697-706
This paper is devoted to a systematic construction of second-order dif
ferential equations invariant under the Poincare, sill!similitude and
conformal groups in three-dimensional spacetime. A classification of a
ll possible realizations of the Lie algebras under the action of the g
roup of local diffeomorphisms of R-4 is presented. Then by means of th
e differential invariants the most general invariant differential equa
tions of second order are constructed.