Reductions and exact solutions of a nonlinear Dirac equation

Ansätze are constructed which reduce the Poincaré-invariant equation for the spinor field $\Psi (x_0, x_1, x_2, x_3)$ to a system of partial differential equations for the four-component function $\varphi(\omega)$ depending on three invariant variables $\omega=\{\omega_1(x), \omega_2(x), \omega_3(x)\}$. Multiparameter families of exact solutions of the nonlinear Dirac equation with the mass term are found. The $P(1.3)$-nonequivalent Ansätze for a vector field are constructed.