Персона: Кутуков, Александр Алексеевич
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Кутуков
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Александр Алексеевич
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- ПубликацияТолько метаданныеApplication of a Computer Algebra System for Constructing Newton Polygons for Ordinary Differential Equations(2020) Kudryashov, N. A.; Kutukov, A. A.; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич© 2020, Springer Nature Switzerland AG.Newton polygons corresponding to nonlinear ordinary differential equations of polynomial form help visually determine some properties of differential equations. In particular, the Newton polygons are used at finding asymptotic and exact solutions of nonlinear differential equations. In this report we present the algorithm of the ACNP (automatic construction of Newton polygons) program for the automatic construction of the Newton polygons corresponding to ordinary differential equations. The program has been written in Maple symbolic computing environment. The input to the program is a polynomial ordinary differential equation. The output is a set of points on the plane corresponding, according to a certain rule, to the monomials of the differential equation, the Newton polygon and the pole order of the solution for the differential equation. The application of the ACNP program has been demonstrated for studying the integrability property and for finding exact and asymptotic solutions of nonlinear differential equations.
- ПубликацияОткрытый доступAutomation of the construction of the soliton solutions of nonlinear Schrodinger-type equations(2020) Kutukov, A. A.; Kudryashov, N. A.; Кутуков, Александр Алексеевич; Кудряшов, Николай Алексеевич© Published under licence by IOP Publishing Ltd.An algorithm for constructing solitary wave solutions of nonlinear ordinary differential equations which is a variation of the simple equations method has been considered. The program was written in the Maple computer algebra system. The program has been tested on equations describing the propagation of pulses in an optical fiber.