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