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Кутуков, Александр Алексеевич

Организационные подразделения

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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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Только метаданные
Properties of the generalized Chavy-Waddy–Kolokolnikov model for description of bacterial colonies
(2024) Kudryashov, N. A.; Kutukov, A. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич; Лаврова, София Федоровна
The Chavy-WaddyвЂ“Kolokolnikov model with dispersion for describing bacterial colonies is considered. This mathematical model is described by a nonlinear partial differential equation of the fourth order. This equation does not pass the PainlevГ© test and the Cauchy problem cannot be solved by the inverse scattering transform. Some new properties of the Chavy-WaddyвЂ“Kolokolnikov model are studied. Analytical solutions of the equation in traveling wave variables are found taking into account the dispersion coefficient. It is shown that, unlike the model without dispersion, a bacterial cluster can move, which allows us to consider dispersion as some kind of control for bacterial colony. Using numerical modeling, we also demonstrate that the initial concentration of bacteria in the form of a random distribution over time transforms into a periodic wave, followed by a transition to a stationary solitary wave without taking dispersion into account.
Только метаданные
Periodic and solitary wave solutions of the Biswas-Arshed equation for pulses in a birefringent fiber
(2021) Kutukov, A. A.; Kudryashov, N. A.; Prikazchikova, A. S.; Кутуков, Александр Алексеевич; Кудряшов, Николай Алексеевич
© 2021 Institute of Physics Publishing. All rights reserved.The system of coupled generalized nonlinear Schrödinger equations describing the propagation of pulses in a birefringent fiber is considered. Using the traveling wave reduction of the system constraints on the model parameters are found, which are the compatibility conditions for the system. Under the found constraints on the parameters, solutions of the system in the form of periodic and solitary waves are obtained.
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ПРЕОБРАЗОВАНИЯ НЕКОТОРЫХ НЕЛИНЕЙНЫХ УРАВНЕНИЙ С ПЕРЕМЕННЫМИ КОЭФФИЦИЕНТАМИ
(2023) Грибов, П. А. ; Кудряшов, Н. А. ; Кутуков, А. А. ; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич
Представлены преобразования для нелинейных уравнений в частных производных с переменным коэффициентом. Показано, что свойства интегрируемости для некоторых уравнений с переменными коэффициентами выполняются естественным образом, так как эти уравнения преобразуются к хорошо известным интегрируемым уравнениям в частных производных.
Только метаданные
Application 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.
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Automation 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.
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ЧИСЛЕННОЕ ИССЛЕДОВАНИЕ ОБОБЩЕННОЙ МОДЕЛИ ЧАВИ–ВАДДИ–КОЛОКОЛЬНИКОВА
(НИЯУ МИФИ, 2023) Кутуков, А. А.; Кудряшов, Н. А.; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич
Рассматривается обобщенное уравнение Чави–Вадди–Колокольникова, которое описывает нелинейные физические и биологические процессы, в частности движение бактерий при воздействии раздражителей. Численное исследование модели проводится с использованием псевдоспектрального метода. Для тестирования программы применяются точные решения обобщенного уравнения Чави–Вадди–Колокольникова. Для численного моделирования используются начальные условия в виде периодических и уединенных волн, а также в виде белого шума. Приводятся графики результатов численного моделирования. Показано, что при различных значениях параметров модели происходит формирование периодических структур
Только метаданные
On solutions of one of the second-order nonlinear differential equation: An in-depth look and critical review
(2022) Kudryashov, N. A.; Kutukov, A. A.; Lavrova, S. F.; Safonova, D. V.; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич; Лаврова, София Федоровна; Сафонова, Дарья Владимировна
© 2022 Elsevier GmbHA critical review of recent articles by two scientific groups, which have considered a well-known nonlinear differential equation of the second order, is presented. One of these groups is led by G. Akram et. al. from Pakistan (Department of mathematics, University of the Punjab, Lahore). Another group is led by K.-J. Wang from China (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo). In a number of papers published by these authors there have been presented a lot of solutions of the well-known differential equation. In fact, this differential equation was studied more than 150 years ago in the works of outstanding mathematicians Niels Henrik Abel (1827), Karl Gustav Jacob Jacobi (1829) and Karl Weierstrass (1855, 1862). However, the scientific groups of Akram and Wang, apparently not being familiar with the works of prominent mathematicians and not realizing that this equation has a unique solution on the complex plane, have been trying to rewrite the solution of this equation using symbolic mathematics programs misleading by that the scientific community. Although there are several erroneous works by Akram and Wang, only a few articles are analyzed here. The errors of a few works by these authors are discussed. The correct solutions of this popular equation, which is often encountered in nonlinear optics, are presented.
Только метаданные
Traveling Wave Solutions of the Coupled Nonlinear Schrodinger Equation with Cubic-quintic-septic and Weak Non-local Nonlinearity
(2022) Kutukov, A. A.; Kudryashov, N. A.; Кутуков, Александр Алексеевич; Кудряшов, Николай Алексеевич
© 2022 American Institute of Physics Inc.. All rights reserved.The generalized coupled nonlinear Schrödinger equation with cubic-quintic-septic and weak non-local nonlinearity describing the signal propagation in an optical fiber has been considered. Four ordinary differential equations have been obtained using traveling wave variables. The considering equations are reduced to the nonlinear ordinary differential equation of the first order and second degree taking into account the compatibility conditions. The general solution of the obtained equation has been found under some constraints on the parameters of the model.
Только метаданные
Optical solitons for the concatenation model: Power-law nonlinearity
(2023) Kudryashov, N. A.; Kutukov, A. A.; Biswas, A.; Zhou, Q.; Кудряшов, Николай Алексеевич; Кутуков, Александр Алексеевич
Только метаданные
Automation of Processes Related to the Modeling of Equilibrium Configurations of Point Vortices
(2023) Kutukov, A. A.; Kudryashov, N. A.; Кутуков, Александр Алексеевич; Кудряшов, Николай Алексеевич