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A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Czasopismo
Rocznik
Tom
Strony
187--195
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
autor
autor
autor
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, Cracow 30-059 Poland [Prykarpatsky, A. K.], prykanat@cybergal.com ; prikarpa@wms.mat.agh.edu.pl
Bibliografia
- [1] V.E. Zakharov, The Benney equations and the quasiclassical approximation in the inverse scattering transform, Func. Anal. 14 (1980), 15–24 (in Russian).
- [2] J. Gibbon, Collisionless Boltzmann equations and integrable moment equations, Physica 3D (1981), 502–511.
- [3] N.N. Bogoliubov, N.N. Bogoliubov (Jr.), Introduction to Quantum Statistical Mechanics, Nauka, Moscow, 1984 (in Russian).
- [4] N.N. Bogoliubov, Lectures on Statistical Mechanics, Nauka, Moscow, 1982, 270–297 (in Russian).
- [5] L.M. Brehovski, V.V. Goncharov, Introduction to Solid State Mechanics, Nauka, Moscow, 1982 (in Russian).
- [6] Yu.A. Mitropolski, N.N. (Jr.) Bogoliubov, A.K. Prykarpatsky, V.Hr. Samoilenko, Integrable Dynamical Systems, Nauka dumka, Kiev, 1987 (in Russian).
- [7] N.N. (Jr.) Bogoliubov, A.K. Prykarpatsky, Quantum method of Bogoliubov generating functionals: Lie algebra of currents, its representation and functional equations, Physicsof Elementary Particles and Atom Nucleus 17 (1986), 799–827 (in Russian).
- [8] A.K. Prykarpatsky, I.V. Mykytiuk, Algebraic Aspects of Integrability of Nonlinear Dynamical Systems on Manifolds, Naukova dumka, Kiev, 1991 (in Russian).
- [9] B. Kupershmidt, Hydrodynamical Poisson brackets and local Lie algebras, Phys. Lett. 21A (1987), 167–174.
- [10] D.R. Lebedev, Yu.I. Manin, Benney’s long wave equations: Lax representation and conservation laws, Zapiski nauchnykh seminarov LOMI.-1980-96; Boundary Value Problems of Mathematical Physics and Adjacent Function Theory Questions. pp. 169–178 (in Russian).
- [11] P.V. Malyshev, D.Y. Petrina, V.I. Gerasimenko, Mathematical Foundations of Classical Statistical Mechanics: Continuous Systems, Taylor & Francis, 1989
- [12] N.N. Bogoliubov, A.A. Logunov, A.I. Oksak, J.T. Todorov, The General Principles of uantized Field Theory, Nauka, Moscow, 1987.
- [13] B.A. Dubrovin, S.P. Novikov Hydrodynamics of weakly deformable solitonic lattices, Russian Math. Surv. 44 (1989), 29–98.
- [14] J. Cavalcante, H.P. McKean The classical shallow water equations: symplectic geometry, Physica 4D (1982), 253–260.
- [15] J. Verosky Higher-order symmetries of the compressible one-dimensional isentropic fluid equations, J. Math. Phys. 25 (1984), 884–888.
- [16] N.N. Bogoliubov (jr), A.K. Prykarpatsky, V.Hr. Samoylenko The Hamiltonian aspects of hydrodynamical Benney type equations and associated with them Boltzmann-Vlasov equations on axis, Ukr. Phys. Journal 37 (1992), N1, 147–156
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH9-0001-0010