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2013
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# Oleg Bogoyavlenskij

ul. Gubkina 8, Moscow, 119991, Russia
Kingston, K7L 3N6, Canada
V.A. Steklov Institute of Mathematics, Russian Academy of Sciences
Department of Mathematics, Queen’s University

## Publications:

 Bogoyavlenskij O. I., Peng Y. Exact Solutions to the Beltrami Equation with a Non-constant $\alpha({\mathbf x})$ 2021, vol. 26, no. 6, pp.  692-699 Abstract Infinite families of new exact solutions to the Beltrami equation with a non-constant $\alpha({\mathbf x})$ are derived. Differential operators connecting the steady axisymmetric Klein – Gordon equation and a special case of the Grad – Shafranov equation are constructed. A Lie semi-group of nonlinear transformations of the Grad – Shafranov equation is found. Keywords: ideal fluid equilibria, force-free plasma equilibria, Klein – Gordon equation, Yukawa potential, Beltrami equation Citation: Bogoyavlenskij O. I., Peng Y.,  Exact Solutions to the Beltrami Equation with a Non-constant $\alpha({\mathbf x})$, Regular and Chaotic Dynamics, 2021, vol. 26, no. 6, pp. 692-699 DOI:10.1134/S1560354721060071
 Bogoyavlenskij O. I., Reynolds A. P. Criteria for existence of a Hamiltonian structure 2010, vol. 15, no. 4-5, pp.  431-439 Abstract The necessary and sufficient conditions are derived for the existence of a Hamiltonian structure for 3-component non-diagonalizable systems of hydrodynamic type. The conditions are formulated in terms of tensor invariants defined by the metric $h_{ij}(u)$ constructed from the Haantjes (1,2)-tensor. Keywords: Poisson brackets, conformally flat metric, covariant derivatives, Weyl–Schouten equations, Haantjes tensor Citation: Bogoyavlenskij O. I., Reynolds A. P.,  Criteria for existence of a Hamiltonian structure, Regular and Chaotic Dynamics, 2010, vol. 15, no. 4-5, pp. 431-439 DOI:10.1134/S1560354710040039
 Bogoyavlenskij O. I. Integrable Lotka–Volterra systems 2008, vol. 13, no. 6, pp.  543-556 Abstract Infinite- and finite-dimensional lattices of Lotka–Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka–Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions. Keywords: Lax representation, Hamiltonian structures, Casimir functions, Riemannian surfaces, Lotka–Volterra systems, integrable lattices Citation: Bogoyavlenskij O. I.,  Integrable Lotka–Volterra systems, Regular and Chaotic Dynamics, 2008, vol. 13, no. 6, pp. 543-556 DOI:10.1134/S1560354708060051