Exact plane-symmetric solutions of nonlinear equations of a spinor field in the theory of gravitation

Summary (translated from the Russian): "We obtain exact plane-symmetric solutions of spinor field equations with nonlinear terms that are arbitrary functions of the invariant S=overline psi psi taking into account the self-gravitational field. We formulate conditions under which the original system of Einstein equations and of spinor field equations with a power nonlinearity has regular solutions with localized (negative) spinor field energy density---soliton-like solutions. We also obtain exact solutions of the above-mentioned spinor field equations in flat space-time. We show that the original system of equations does not have soliton-like solutions. This means that the self-gravitational field plays a decisive, regularizing role in the formation of soliton-type solutions of the nonlinear spinor field equations."