The symmetry reduction of the system $∇u_i = F_i(u_1, u_2), i = 1, 2$, to the system of the ordinary differential equations (ODE) about the subgroups of the extended Poincare group is carried. The 29 systems of the ODE for each of the 5 earlier discovered representations of the dilatation operator $D$ were obtained.

[1] Dirac P.A.M. The relation between mathematics and physics // Proceedings of the Royal Society. Edinburgh. A. - 1938-1939. - 59 . - P.122-129.

[2] Zhdanov R.Z., Fushchych W.I., Marko P. V. New scale-invariant nonlinear equations for a complex scalar field // Physica D 95. - 1996. - P.158-162.

[3] Fushchych V.I., Barannik L.F., Barannik A.F. Subgroup analysis of Galileo and Poincare groups and reduction of nonlinear equations. - K.: Nauk. Dumka, 1991. - 304 p.

[4] Fushchych V.I., Shtelen V.M., Serov N.I. Symmetry analysis and exact solutions of equations of mathematical physics. - K.: Naukova Dumka, 1989. - 336 p.

[5] Barannik L.F. On symmetry reduction and exact solutions of the nonlinear d'Alembert equation / / Symmetry and exact solutions of equations of mathematical physics. - K.: Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR, 1989. - P.11-13.

[6] Fushchych V.I., Barannik A.F. On exact solutions of the nonlinear d'Alembert equation in the Minkowski space $R_{1, n}$ // Reports of the Academy of Sciences of the Ukrainian SSR. Series. A. - 1990. - N 6. - P. 31-34.

[7] Fushchych V.I., Barannik A.F. Maximal subalgebras of rank $n-1$ of the algebra $AP(1, n)$ and reduction of nonlinear wave equations. 1. // Ukr. mat-mat. zhurn. - 1990. - 42, N 11. - P. 1250-1256.