Yuri Rybakov
Doctor of Physics and Mathematics

"In scientific research, you can’t stop at what has been achieved."

1956 - 1962

Studied at the Faculty of Physics of Lomonosov Moscow State University, the Department of Theoretical Physics, specialty - “Physicist”.

1962 - 1965

Postgraduate student of Lomonosov Moscow State University, the Department of Theoretical Physics, in 1965 thesis on “Problems of stability in nonlinear field theory” for the degree of Candidate of Physical and Mathematical Sciences in the specialty “Theoretical Physics” was defended.

1964 - 1972

Assistant of the Department of Theoretical Physics at Peoples’ Friendship University named after P. Lumumba (now RUDN University).

1972 - 2017

Associate professor of the Department of Theoretical Physics of Peoples’ Friendship University named after P. Lumumba (now RUDN University). From 1994 - Head of the Department of Theoretical Physics of RUDN University.


Thesis on “Stability of multidimensional solitons” for the degree of Doctor of Physical and Mathematical Sciences in the specialty “Theoretical Physics” was defended at the Joint Institute for Nuclear Research (Dubna).


Honorary title “Honored Scientist of the Russian Federation” was awarded by the decree of the President of the Russian Federation for the development of priority areas of science and technology.


Honorary badge “Veteran of the RUDN” for many years of conscientious work was awarded.

2017 - present

Professor at the Research Institute of Physics and Technology of RUDN University.


Gives lectures to physics students of the RUDN University:

  • “Group theory”;
  • “Classical and quantum field theory”;
  • “Foundations of quantum chromodynamics”;
  • “String theory”;
  • “Mathematical methods in physics”.

The author of monographs and study guides:

  1. Rybakov Yu.P. “Foundations of Quantum Electrodynamics, Chromodynamics and String Theory”. - M.: RUDN, 2014. - 112 pp.
    The course outlines the basic principles of quantum electrodynamics and chromodynamics needed to describe the electromagnetic and strong interactions of elementary particles.
  2. Makhankov V.G., Rybakov Y.P., Sanyuk V.I. “The Skyrme Model. Fundamentals, Methods, Applications”. New York: Springer-Verlag, 2013. - 260 pp.
    This reference book is the first to present the amazing depth and inherent beauty of the Skyrme model approach, which strongly influenced progress in nonlinear mathematical physics. After an evaluation of the model as given in Skyrme’s pioneering papers, a thorough overview of the problems is presented that will also serve as an introduction to both researchers and advanced undergraduate students specializing in high energy physics.


  • Obtained a generalization of the Hobart-Derrick theorem on the energy instability of stationary non-topological solitons for a space dimension greater than two.
  • Found sufficient Q-stability conditions for multicharged stationary solitons for any regular Lagrangian model with a compact inner group.
  • Proved the existence, smoothness, and absolute stability of a spherically symmetric soliton solution with a unit topological charge for the SU(2) chiral Skyrme model (including taking into account the non - Abelian gauge field). In the case of solitons with higher topological charges, the existence of a stable axially symmetric configuration that implements the minimum energy was proved.
  • Proved the existence of stable axially symmetric solitons with a nontrivial Hopf index, and also established the existence of string-like solutions approximating them for the S2 nonlinear Faddeev sigma-model.
  • Established the global stability of monotonic electron energy distributions and the instability of nonmonotonic distributions for the equilibrium Bernstein-Green-Kruskal configurations in the Vlasov-Poisson plasma.
  • Found a necessary and sufficient condition for the stability of Wheeler wormholes in nonlinear electrodynamics.
  • Constructed a 16-spinor implementation of Skyrme-Faddeev chiral model and, based on the Brioschi identity, gave a classification of topological solitons in the lepton and baryon sectors.
  • Constructed a spinor implementation of the chiral graphene model and established the anisotropy of the magnetic properties of monolayer and bilayer graphene.
  • Studied the magnetic and mechanical properties of carbon nanotubes in the framework of the chiral graphene model.

Scientific interests

  • Stability of multidimensional solitons;
  • Nonlinear field theory;
  • Theory of gravity;
  • Condensed matter physics;
  • Graphene-like states;
  • Carbon nanotubes and fullerenes;
  • Filtration theory (hydrodynamics of flows in porous media);
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 lacks asymptotic flatness) and some examples with spinor field nonlinearities.
We study the filtration process in porous media and compare the filtration coefficients for two possible geometries of flows: cylindrical and radial ones. Solving balance equations for impurity concentration in the simplest axially-symmetric stationary case, one finds the radial filtration process more effective. Therefore, we restrict our attention to the radial filters with non-homogeneous grain filling. First, we describe the transverse diffusion effect and then suggest the generalization of the Darcy’s filtration law, its dynamical origin being stressed. Using the perturbation method, we find the structure of the Stokes stream function for some particular choices of the porosity.
Taking into account the - hybridization effect for valence electrons in carbon atoms, we introduce a unitary matrix as an order parameter and suggest a scalar chiral model of graphene for the description of graphene-like configurations. Using the well-known hedgehog ansatz for modeling Fullerene , we estimate the polarizability of a single Fullerene specie in a uniform external electric field. Finally, we use this result for calculating the parameters of the van der Waals potential for the two interacting Fullerene species.
We consider the generalization of the scalar chiral model of graphene, the 8-spinor field being included for the description of spin and quasi-spin excitations. The invariant Lagrangian density quadratic in derivatives is constructed using the principle of energy positivity and that of correspondence with the scalar model. The electromagnetic interaction is included through the extension of derivatives, the Pauli direct interaction term being added. We consider in detail an example of interaction with the external uniform static magnetic field.
Graphene is basically a single atomic layer of graphite; an abundant mineral which is an allotrope of carbon that is made up of very tightly bonded carbon atoms organized into a hexagonal lattice. The incorporation of magnetism to the long list of graphene capabilities has been pursued since its first isolation. In this contribution, we examine the magnetic possibilities in graphene using the chiral model. In the framework of the 8-spinor generalization of the scalar chiral model of graphene, we consider the spin and quasi-spin excitations in graphene, the interaction of graphene with uniform magnetic field and use the gauge invariance principle for introducing the electromagnetic interaction. The Lagrangian density of the model is simplified and our graphene material reveals the evident diamagnetic effect: the weakening of the magnetic field within the graphene sample. Therefore, graphene can become an ideal material for studying spin transport (spintronics).
Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the ½ -spin particles.
We discuss the 16-spinor field realization of Skyrme - Faddeev chiral model of baryons and leptons as topological solitons. The main idea behind this paper consists in unifying the approaches, suggested by Skyrme and Faddeev for description of baryons and leptons respectively, by using the special 8-semispinor identity invented by the Italian geometer F.~Brioschi. The peculiar property of this unified model is the necessity of generalizing the Einstein gravitational theory by including Kretschmann invariant (i. e. Riemann curvature tensor squared) in the Lagrangian through special structure of the Higgs potential implying the spontaneous breaking of symmetry. This fact reveals the two consequences. The first one concerns the essential role of higher derivatives of the metric tensor at small distances (strong gravity), and the second one concerns the behavior of the model at large distances implying the correspondence with Quantum Mechanics. We consider axially-symmetric states in lepton and baryon sectors and demonstrate the method for calculating topological charges. We give also the definition of the wave function for extended particles – solitons in special stochastic representation, which is illustrated by the famous T.~Young's experiment with n slits and also by spin--statistics correlation as natural consequence of this representation.