Arthemy V. Kiselev

Bio: Arthemy V. Kiselev is an academic researcher from University of Groningen. The author has contributed to research in topics: Lie algebra & Poisson manifold. The author has an hindex of 14, co-authored 110 publications receiving 705 citations. Previous affiliations of Arthemy V. Kiselev include Moscow State University & Ivanovo State Power University.

Algebraic properties of Gardner’s deformations for integrable systems

Abstract: We formulate an algebraic definition of Gardner’s deformations for completely integrable bi-Hamiltonian evolutionary systems. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and hyperbolic Liouville-type systems. We find an exactly solvable two-component extension of the Liouville equation.

Hamiltonian flows on Euler-type equations

Abstract: We analyze properties of Hamiltonian symmetry flows on hyperbolic Euler-Liouville-type equations e ′EL. We obtain the description of their Noether symmetries assigned to the integrals of these equations. The integrals provide Miura transformations from e′EL to the multicomponent wave equations e. Using these substitutions, we generate an infinite-Hamiltonian commutative subalgebra \(\mathfrak{A}\) of local Noether symmetry flows on e proliferated by weakly nonlocal recursion operators. We demonstrate that the correspondence between the Magri schemes for \(\mathfrak{A}\) and for the induced “modified” Hamiltonian flows \(\mathfrak{B}\) ⊂ sym e ′EL is such that these properties are transferred to \(\mathfrak{B}\) and the recursions for e′ EL are factored. We consider two examples associated with the two-dimensional Toda lattice.

Variational Lie algebroids and homological evolutionary vector fields

Abstract: We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.

Renormalization of the Abelian Higgs-Kibble Model

Abstract: This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

Theory of nonlinear lattices

Abstract: 1. Introduction.- 1.1 The Fermi-Pasta-Ulam Problem.- 1.2 Henon-Heiles Calculation.- 1.3 Discovery of Solitons.- 1.4 Dual Systems.- 2. The Lattice with Exponential Interaction.- 2.1 Finding of an Integrable Lattice.- 2.2 The Lattice with Exponential Interaction.- 2.3 Periodic Solutions.- 2.4 Solitary Waves.- 2.5 Two-Soliton Solutions.- 2.6 Hard-Sphere Limit.- 2.7 Continuum Approximation and Recurrence Time.- 2.8 Applications and Extensions.- 2.9 Poincare Mapping.- 2.10 Conserved Quantities.- 3. The Spectrum and Construction of Solutions.- 3.1 Matrix Formalism.- 3.2 Infinite Lattice.- 3.3 Scattering and Bound States.- 3.4 The Gel'fand-Levitan Equation.- 3.5 The Initial Value Problem.- 3.6 Soliton Solutions.- 3.7 The Relationship Between the Conserved Quantities and the Transmission Coefficient.- 3.8 Extensions of the Equations of Motion and the Kac-Moerbeke System.- 3.9 The Backlund Transformation.- 3.10 A Finite Lattice.- 3.11 Continuum Approximation.- 4. Periodic Systems.- 4.1 Discrete Hill's Equation.- 4.2 Auxiliary Spectrum.- 4.3 Relation Between ?j (k) and ?j (0).- 4.4 Related Integrals on the Riemann Surface.- 4.5 Solution to the Inverse Problem.- 4.6 Time Evolution.- 4.7 A Simple Example (A Cnoidal Wave).- 4.8 Periodic System of Three-Particles.- 5. Application of the Hamilton-Jacobi Theory.- 5.1 Canonically Conjugate Variables.- 5.2 Action Variables.- 6. Recent Advances in the Theory of Nonlinear Lattices.- 6.1 The KdV Equation as a Limit of the TL Equation.- 6.2 Interacting Soliton Equations.- 6.3 Integrability.- 6.4 Generalization of the TL Equation.- 6.5 Two-Dimensional TL.- 6.6 Bethe Ansatz.- 6.7 The Thermodynamic Limit.- 6.8 Hierarchy of Nonlinear Equations.- 6.9 Some Numerical Results.- Appendices.- Simplified Answers to Main Problems.- References.- List of Authors Cited in Text.

Spatial tessellations. Concepts and Applications of Voronoi diagrams

Abstract: Definitions and basic properties of the Voronoi diagram generalizations of the Voronoi diagram algorithms for computing Voronoi diagrams poisson Voronoi diagrams spatial interpolation models of spatial processes point pattern analysis locational optimization through Voronoi diagrams.