Kalashnikov E. V.1, Plotnikova V. I.1, Nadakhovskaya M. A.1, Gannibal M. A.2
1Federal State University of Education, Moscow, Russia
2Geological Institute, Kola Science Centre RAS, Apatity, Russia
Email: ekevkalashnikov1@gmail.com, vera_askerova@mail.ru, nadahovskayamarina_fmf@mail.ru, m.a.gannibal@gmail.com
The motion of a foreign atom (e. g. hydrogen or helium isotope) along the interstitials in a diamond-like silicon lattice is considered. The Lagrangian of the system "foreign atom + crystal" accounts for the influence of a foreign atom on the lattice atoms. The symmetries assumed by the Lagrange function allow the multidimensional system of equations describing the behavior of a foreign atom and lattice atoms to be reduced to a one-dimensional nonlinear equation. The solution to the equation is either the Frenkel-Kontorova soliton, which describes the translational behavior of a collective consisting of the foreign atom and the accompanying reversible displacements of the nearest lattice atoms, or the vibrational motion of a foreign atom, as a particle with the mass of an atom. Keywords: Lagrange function, bilinear form, Frenkel-Kontorova soliton.
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