On new relativistically invariant nonlinear equations in two-dimensional space-time

We have constructed new realizations of Lie algebras of the Poincaré and extended Poincaré groups by Lie vector fields. These realizations together with the ones obtained by Rideau and Winternitz, give a complete description of inequivalent representations of the Poincaré, extended Poincaré and conformal algebras within the class of Lie vector fields with two independent and one dependent variables. We have complemented also the set of relativistically invariant second-order scalar differential equations in two-dimensional spacetime obtained by Rideau and Winternitz.