Алгоритм класифікації інтегрованості нелінійних динамічних систем методами комп’ютерної алгебри: Fìz.-mat. model. ìnf. tehnol. 2021, 32:7-12

• Datum: 2021
• Hauptverfasser: Fil, Bohdan, Pelekh, Yaroslav, Vovk, Myroslava, Beregova, Halyna, Magerovska, Tatiana, Pukach, Pavlo
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Schlagworte: система комп'ютерної алге; Wolfram Mathematica; нелінійне хвильове рівняння; закони збереження; інтегральність нелінійних динамічних систем; збережена енергія; рівняння Кортевега — де Фріза
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/150
• Назва журналу: Physico-mathematical modeling and informational technologies

There is developed an algorithm to classify integrable nonlinear dynamical systems via Wolfram Mathematica. The hierarchy of conservation laws for the nonlinear dynamical system can be cal-culated by this algorithm. There are demonstrated some modifications of nonlinear Korteweg-de Vries equations integrated by inverse scatering method. References Olver, P. J. (1986). Applications of Lie Groups to Differential Equations. New York: Springer-Verlag. Mitropol'skiy, Yu. A., Bogolyubov, N. N., Prikarpatskiy, A. K., Samoylenko, V. G. (1987). Integriruyemyye dinamicheskiye sistemy: spektral'nyye i differentsial'no-geometricheskiye aspekty. K.: Naukova dumka. Sanders, J. A., Roelofs, M. (1994). An algorithmic approach to conservation laws using the 3-dimensional Heisenberg algebra. Tech. Rep. 2 RIACA. Sanders, J. A., Wang, J. P. (1995). On the (non)existence of conservation laws for evolution equations. Tech. Rep. WS-445. Amsterdam : Vrije Universiteit. Wolf, T., Brand, A., Mohammadzadeh, M. (1999). Computer algebra algorithms and routines for the computa¬tions of conservation laws and fixing of gauge in differential expressions. J.Symb.Comp., 27, 221-238. DOI doi.org/10.1006/jsco.1998.0250 Göktas, Ü., Hereman, W. (1996). Symbolic computation of conserved densities for systems of nonlinear evolution equations. Technical Report MCS-96-06. Colorado School of Mines. DOI doi.org/10.1006/jsco.1998.0250 Ruo-Xia, Yao, Zhi-Bin, Li. (2006). CONSLAW: A Maple package to construct the conservation laws for nonlinear evolution equations. Applied Mathematics and Computation, 173, 616-635. DOI doi.org/10.1016/j.amc.2005.04.049 Prykarpats'kyy, A. K., Fil', B. M. (1992). Category of topological jet manifolds and certain applications in the theory of nonlinear infinite-dimensional dynamical systems. Ukrainian Mathematical Journal, 44(9), 1136-1148. DOI doi.org/10.1016/j.amc.2005.04.049 Mitropol'skii, Yu. O., Prikarpats'kii, A. K., Fil', B. M. Some aspects of a gradient holonomic algorithm in the theory of integrability of nonlinear dynamic systems and computer algebra problems. Ukrainian Mathematical Journal, 43(1), 63-74. DOI doi.org/10.1007/bf01066906 Fil', B. N., Prikarpatskii, A. K., Pritula, N. N. 1988. Quantum lie algebra of currents - The universal algebraic structure of symmetries of completely integrable dynamical systems. Ukrainian Mathematical Journal, 40(6), 645-649. DOI doi.org/10.1007/bf01057184 Samoilenko, V. G., Fil', B. N. 1988. Algebras of symmetries of completely integrable dynamical systems. Ukrainian Mathematical Journal, 40(2), 164-168. DOI doi.org/10.1007/bf01056471 Pukach, P. Y. 2012. On the unboundedness of a solution of the mixed problem for a nonlinear evolution equation at a finite time, Nonlinear Oscillations, 14(3), 369-378. DOI doi.org/10.1007/s11072-012-0164-6 Fil', B., Pritula, M. 1991. Primeneniye metodov kompyuternoy algebry k nakhozhdeniyu invariantov nelineynykh dinamicheskikh sistem. Tezisy dokladov nauchno-tekhnicheskoy konferentsii "Primeneiye vycheslitel'noy tekhniki i matematicheskikh metodov v nauchnykh iekonomicheskikh issledovaniyakh".