Nonlinear spinor field equations in gravitational theory: plane-symmetric soliton-like solutions

Summary: "We obtain exact plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of S=overlinepsipsi, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). In this case a soliton-like configuration has negative energy. The spinor field equation with a polynomial nonlinearity has a regular solution with positive energy. We also obtain exact solutions to the above spinor field equations in flat space-time. It is shown that in this case soliton-like solutions are absent."