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Solitons with spherical and/or cylindrical symmetry in the interacting system of scalar, electromagnetic, and gravitational fields have been obtained. As a particular case it is shown that the equations of motion admit a special kind of solution with a sharp boundary, known as droplets. For these solutions, the physical fields vanish and the space-time is fiat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero.

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We discuss the static, spherically symmetric Einstein-spinor field system in the possible presence of various spinor field nonlinearities. We take into account that the spinor field energy-momentum tensor (EMT) has in general some off-diagonal components, whose vanishing due to the Einstein equations substantially affects the form of the spinor field itself and the space-time geometry. In particular, the EMT structure with any spinor field nonlinearities turns out to be the same as that of the EMT of a minimally coupled scalar field with a self-interaction potential. Therefore many results previously obtained for systems with such scalar fields are directly extended to the Einstein-spinor field system. Some special solutions are obtained and discussed, in particular, a solution for the Einstein-Dirac system (which lack asymptotic flatness) and some examples with spinor field nonlinearities.1

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The Einstein -de Broglie particle-soliton concept is applied to simulate stationary states of an electron in a hydrogen atom. According to this concept, the electron is described by the localized regular solutions to some nonlinear equations. In the framework of Synge model for interacting scalar and electromagnetic fields a system of integral equations has been obtained, which describes the interaction between charged 3D soliton and Coulomb center. The asymptotic expressions for physical fields, describing soliton moving around the fixed Coulomb center, have been obtained with the help of integral equations. It is shown that the electron-soliton center travels along some stationary orbit around the Coulomb center. The electromagnetic radiation is absent as the Poynting vector has nonwave asymptote O(r −3 ) after averaging over angles, i.e. the existence of spherical surface corresponding to null Poynting vector stream, has been proved. Vector lines for Poynting vector are constructed in asymptotical area.

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