Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8422Research ArticleTopological Soliton Configurations in 8-Spinor Nonlinear ModelRybakovYu PDepartment of Theoretical Physicssoliton4@mail.ruFarrajN AbiDepartment of Theoretical Physics-UmniyatiYuDepartment of Theoretical Physics-Peoples’ Friendship University of Russia15032013312913608092016Copyright © 2013,2013We study the structure of the charged topological solitons in the lepton sector of the nonlinear 8-spinor model, at small distances the closed-string approximation being used. The mass, the spin and the magnetic moment of the soliton configuration with the unit leptonic number are estimated. The model is based on the well-known 8-spinor identity suggested by the Italian geometer Brioschi. Due to the identity the Dirac current appears to be time-like 4-vector that permits one to introduce the special form of the Higgs potential depending on the current squared. Within the framework of this model the natural classification of leptons and baryons can be realized via the Higgs mechanism. Concentrating on the lepton sector we study the simplest soliton configuration endowed with the unit Hopf index playing the role of the lepton number. Investigating the behavior of solutions at large and small distances we obtain the numerical estimate of physical characteristics of the topological soliton. The special symmetry group is used in our calculation, the combined rotations in ordinary and isotopic spaces being considered. The corresponding equivariant spinor fields involve phase functions linear with respect to azimuthal and toroidal angles. This property permits one to find explicit value of the topological invariant for the axially-symmetric configuration and to investigate the dependence of the physical characteristics on topology.8-spinortopological chargesolitons8-спинортопологический зарядсолитоны[Rybakov Y.P., Farraj N., Umniyati Y. Chiral 8-Spinor Model with Pseudo-Vector Interaction // Bull. of Peoples’ Friendship University of Russia, Series “Mathematics. Information Sciences. Physics”. — 2012. — No 3. — Pp. 138–141.][Faddeev L.D. Gauge-Invariant Model of Electromagnetic and Weak Interactions of Leptons // Reports of Ac. of Sc. USSR. — 1973. — Vol. 210, No 4. — Pp. 807–810.][Skyrme T.H.R.A Unified Field Theory of Mesons and Baryons // Nucl. Phys. — 1962. — Vol. 31, No 4. — Pp. 556–559.][Cartan E. Le.cons sur la th`eorie des spineurs. — Paris: Actualit`es scientifiques et industrielles, 1938. — 223 p.][Rybakov Y.P. Soliton Configurations in Generalized Mie Electrodynamics // Phys. of Nuclei. — 2011. — Vol. 74, No 7. — Pp. 1102–1105.][Burinskii A. Some Properties of the Kerr Solution to Low Energy String Theory // Phys. Rev. D. — 1995. — Vol. 52. — Pp. 5826–5831.][Whitney H. Geometric Integration Theory. — Princeton, New Jersey: Princeton University Press, 1957. — P. 534.][Whitehead J.H.C. An Expression of Hopf’s Invariant as an Integral // Proc. Roy. Irish. Acad. Sci. — 1947. — Vol. 33. — Pp. 117–123.][Mie G. Die Geometrie der Spinoren // Ann. der Physik. — 1933. — Vol. 17, No 5. — Pp. 465–500.]