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Theoretical study of electromagnetic wave propagation knotted


М.V. Smelov – Ph.D. (Eng.), Head of the Electromagnetic Research Department of the NO «Foundation for Advanced Technologies and Innovations»


The article describes the results of theoretical research on the spread of knotted electromagnetic waves induced in the antenna field knotted anechoic conditions. The aim of theoretical research, using topological properties of Hopf of S 2 bundle in the sphere S 3, calculate explicitly function that describes the motion of knotted electromagnetic wave (EMW) in the form of torus knot in a stereographic projection of the field (in the form of electromagnetic vacuum soliton) from S 3 locally on three-dimensional Euclidean space R 3, it is necessary to create a technical transmitting and receiving antennas, it is existing in the space R 3.

The theoretical aspect of the existence of a knotted electromagnetic field based on the findings of theoretical research of new nontrivial topological solutions of Maxwell's equations written in the second exterior differential forms. It is the existence of electromagnetic field described by these equations, due to the phenomenon of the Hopf bundle S 3 hypersphere physical space (vacuum), where the stereographic projection S 3 parallels in each of its points on our observable 3-dimensional Euclidean space has the shape of knotted 3-tori. An topologically non-trivial solution of Maxwell's equations in a vacuum in a system of nonlinear partial differential equations of second order with respect to unknown cards Hopf transformation φ, θ, solved the initial data of the Cauchy. These decisions are a first approximation, the photon pulses describe solitons in the form of torus knots. The published experimental results confirm the conclusions of the theory.

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  2. Ranada A.F. Knotted solutions of the Maxwell equation in vacuum // Journal of Physics. A 23. I.815–L.820. 1990.
  3. Smelov M.V. Jeksperimental'noe issledovanie rasprostranenija zauzlennoj jelektromagnitnoj volny, inducirovannoj zauzlennoj antennoj v naturnyh bezjehovyh uslovijah // Radiotehnika. M. 2016. № 12. S. 189–195.
June 24, 2020
May 29, 2020

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