Yu. P. Rybakov

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian Lint=ϕ,αϕ,αΦ(S), where Φ(S) is an arbitrary function of the invariant S=ψψ, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function Φ(S), and isotropic expansion of the space as t → ∞ is established.

Nonlinear spinor fields in Bianchi-I space: Exact self-consistent solutions

AbstractCalculations are performed to obtain exact self-consistent solutions of nonlinear spinor-field equations with self-action terms in Bianchi-I space. The latter terms are arbitrary functions of the invariant

Self-consistent droplet-like solutions of the equations of the electromagnetic field with induced nonlinearity

s = \overline \psi \psi

Soliton stability in a nonlinear model of quark retention

. A detailed examination is made of equations with exponential nonlinearity, when the nonlinear term in the Lagrangian of the spinor field Ln=λsn. Here, λ is the nonlinearity parameter, n>1. It is shown that these equations have finite solutions and solutions that are singular at the initial moment of time. The singularity is absent in the case of solutions that describe systems of fields for which the energy dominance condition is violated. It is further shown that if the mass parameter m≠0 in the spinor-field equation, expansion of Bianchi-I space becomes isotropic as t → ∞. This does not occur when m=0. Specific examples of solutions of linear and nonlinear spinor-field equations are presented.

String solutions in the S2 nonlinear σ-model with a gauge field

Exact cylindrically symmetric solutions are obtained for a class of interacting scalar and vector fields in a rotating Godel Universe. We select those with the properties of solitons with smooth decrease of the fields to asymptotics and those with sharp boundaries (droplets). It is shown that only some of the droplets are stable with respect to perturbations that preserve cylindrical symmetry.

Fresnel diffraction of solitons in the Synge model

The properties of droplet-like configurations in a system of interacting scalar and electromagnetic fields are investigated, taking into account their own gravitational field, also in the Euclidean limit. Exact regular solutions of the corresponding equations are found, corresponding to zero values for energy and electric charge.

Soliton stability in the Synge model with an electromagnetic field

The generalization of spinor electrodynamics proposed by V. G. Kaldyshevskii, in which distortion of momentum space is taken into account, is considered. In the heavy-particle approximation, the structure of a possible soliton solution of the equations of motion which is invariant relative to a sequence of permissible groups of transformations is established. Numerical estimates of the mass and magnetic moment of the charged state with spin 1/2 are made.

Lyapunov stability of scalar charged solitons

A one-dimensional version of a “soliton pocket” scalar model is considered, illustrating the mechanism of quark retention. The region of parameter variation of the model is found such that a nodeless soliton solution is Lyapunov-stable and the corresponding quark-retention mechanism is effective.