Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions

• Autorzy: Kindybaliuk A. , Prytula M.
• Języki publikacji: EN

Abstrakty

EN

In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.

Słowa kluczowe

EN

nonlinear dynamical system; conservation laws; implectic operators; method of undetermined coefficients; differential algebraic algorithm; combined algorithm; finite dimensional reduction; Hamiltonian system; exact solutions; Boussinesq-Burgers equation

PL

nieliniowy układ dynamiczny; prawa zachowania; algebraiczny algorytm różniczkowy; system Hamiltona; rozwiązania dokładne; równanie Boussinesqa-Burgersa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 3
• Strony: 85--99
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Kindybaliuk A.

• Ivan Franko National University of Lviv Lviv, Ukraine

autor

Prytula M.

• Ivan Franko National University of Lviv Lviv, Ukraine

Bibliografia

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• [2] Tao Chen, The generalized Broer-Kaup-Kupershmidt system and its Hamiltonian extension, Tao Chen, Li-Li Zhu, Lei Zhang, Applied Mathematical Sciences 2011, 5(76), 3767-3780.
• [3] Prykarpatsky A.K., Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds: Classical and Quantum Aspects, A.K. Prykarpatsky, I.V. Mykytiuk, Kluwer, Netherlands 1999, 560 p.
• [4] Hentosh О.E., Differential-geometric and Lie-algebraic Foundations of Integrable Nonlinear Dynamical Systems on Functional Manifolds, О.E. Hentosh, M.M. Prytuka, А.K. Prykarpatsky, Publish Center LNU Franko, Lviv 2006, 408 p. (in Ukrainian).
• [5] Arnold V.I., Mathematical Methods of Classic Mechanics, Nauka, M.: 1979, 431 p. (in Russian).
• [6] Bogoyavlensky O.I., On the connection of hamiltonian formalisms for stationary and nonstationary problems, O.I. Bogoyavlensky, S.P. Novikov, Functional Analysis and Its Applications 1976, 10, 1, 9-15 (in Russian).
• [7] Blackmore D., Nonlinear Dynamical Systems of the Mathematical Physics: Spectral and Differential-geometrical Integrability Analysis, D. Blackmore, A.K. Prykarpatsky, V. Hr. Samoylenko, World Scientific Publ., NJ, USA 2011, 563 p.
• [8] Mytropolsky Ju.А., Integrable dynamical systems: spectral and differential-algebraic aspects, Ju.А. Mytropolsky, N.N. Bogoliubov, А.K. Prykarpatsky, V.Gr. Samoylenko, Nauk. Dumka, K.: 1987, 296 p. (in Russian).
• [9] Prykarpatsky А.K., On the one construction of finite dimensional reductions on functional manifolds, А.K. Prykarpatsky, O.G. Bihun, Math. methods and phis.-mech. fields, 48, 1, 7-14 (in Ukrainian).
• [10] Prykarpatsky А.K., Algebraic Aspects of Integrability of Dynamical Systems on Manifolds, А.K. Prykarpatsky, I.V. Mykytiuk, А.М Samoylenko, Nauk. Dumka, K., 1991, 288 p. (in Russian).
• [11] Samoylenko А.М., Algebraic-analytical Aspects of Complete Integrable Systems and Their Perturbations, А.М. Samoylenko, Ya.А. Prykarpatsky, Institute of Mathematics of NAN Ukraine, К.: 2002, 237 p. (in Ukrainian).