Abstract
This research work is related to soliton solutions considered as models that can describe the complex configuration of elementary particles from the study of the interactions of their fields. It is interested in the interaction of fields between two different elementary particles by expressing their physical properties. For that, we have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function P(I). It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density. Moreover, the total charge of particles is finite and the total energy of the interaction fields is bounded. It have been emphasized the importance to the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions. In flat space-time, soliton-like solutions exist but the total energy of the interaction fields is equal to zero. We have also shown that in the linear case, soliton-like solutions are absent.
Highlights
The exact solutions of nonlinear differential equations to describe physical phenomena have become a scientific priority after the development of general relativity (GR) and quantum field theory (QFT)
We have obtained, exact static plane symmetric soliton-like solutions to the nonlinear equations of interacting electromagnetic and scalar fields taking into account the own gravitational field of elementary particles using the calibrated invariance function P ( I )
It has been proved that all solutions of the Einstein, nonlinear electromagnetic and scalar field equations are regular with the localized energy density
Summary
The exact solutions of nonlinear differential equations to describe physical phenomena have become a scientific priority after the development of general relativity (GR) and quantum field theory (QFT). The aim of this paper is to determine the exact static plane symmetric soliton-like solutions to nonlinear interacting electromagnetic and scalar field equations taking into account the own gravitational field of the elementary particles by using the calibrated invariance function P= ( I ) P0 ( N − λI ) under the conditions N > λI , P ( I ) = 0 in x = 0 , while specifying the width and depths of localization of the energy density.
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