Reduction of a multidimensional poincare-invariant nonlinear equation to two-dimensional equations

We study the structure of the invariants of the extended isochronous Galilean algebra which is a subalgebra of the Poincaré algebra AP(1, n). Using these results we classify maximal subalgebras of rank n–2 and n–1 of AP(1, n). With respect to subalgebras of rank n–1 of AP(1, n) ansatzes are constructed reducing the equation (u, (u)², u)=0 to differential equations in two invariant variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1311–1323, October, 1991.