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Лаврова, София Федоровна

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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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Лаврова

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София Федоровна

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Теперь показываю 1 - 9 из 9

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
Traveling wave solutions of the derivative nonlinear Schrodinger hierarchy
(2024) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
Только метаданные
Dynamical features of the generalized Kuramoto-Sivashinsky equation
(2021) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
© 2020 Elsevier LtdThe stabilizing effects of dispersion on the dynamics of the generalized Kuramoto-Sivashinsky equation at various degrees of nonlinearity are considered in this paper. The second and third sections investigate properties of the traveling wave reduction of the Kuramoto-Sivashinsky equation. In the fourth section the changing dynamics of the generalized KuramotoSivashinsky PDE is explored by calculating the largest Lyapunov exponents over a range of values of the dispersion parameter.
Только метаданные
Dynamical properties of the generalized model for description of propagation pulses in optical fiber with arbitrary refractive index
(2021) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
© 2021 Elsevier GmbHA partial differential equation for description of pulse propagation in optical fiber with arbitrary refractive index is considered. Using Melnikov method, an analytical condition for the existence of horseshoe chaos is obtained for the traveling wave reduction of the investigated equation. A way to control chaos in the dynamical system is proposed. An analytical prediction is tested numerically by plotting basins of attraction.
Только метаданные
Complex dynamics of perturbed solitary waves in a nonlinear saturable medium: A Melnikov approach
(2022) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
© 2022 Elsevier GmbHObjective: To investigate the nonlinear dynamics of a periodically perturbed second-order ordinary differential equation obtained by using traveling wave variables in the model of pulse propagation in a nonlinear medium with saturation. Method: The Melnikov function of the investigated system along its homoclinic and heteroclinic orbits is constructed. It is established that the necessary condition for the occurrence of Melnikov chaos is always met. By analogy with the well-known Duffing equation, a damping term is added to the system to control chaos. Using the numerical calculation of the Melnikov integrals, conditions are found on the parameters of the new system for which the Melnikov chaos takes place. To verify the results obtained by the Melnikov method, attraction basins of the system are constructed. Results: The results obtained by the Melnikov method go in agreement with the structure of the constructed basin boundaries.
Только метаданные
Nonlinear Dynamical Regimes of the Generalized Kuramoto-Sivashinsky Equation with Various Degrees of Nonlinearity
(2022) Lavrova, S. F.; Kudryashov, N. A.; Лаврова, София Федоровна; Кудряшов, Николай Алексеевич
© 2022 American Institute of Physics Inc.. All rights reserved.The stabilizing effects of dispersion on the dynamics of the generalized Kuramoto equation with three different degrees of nonlinearity are considered. The second and third sections investigate the traveling wave reduction of the studied equation. The fourth section explores the changing dynamics of the generalized Kuramoto–Sivashinsky PDE by calculating its largest Lyapunov exponents over a range of values of the dispersion parameter.
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
Dynamical properties of the periodically perturbed Triki–Biswas equation
(2022) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
© 2021In this paper, a perturbed traveling wave reduction of the Tricky–Biswas equation, which is used to describe the propagation of pulses in nonlinear optics, is considered. A stability analysis of the investigated ODE system without perturbation is carried out. The Melnikov function along the homoclinic orbit is constructed. It is found that in the studied system the necessary condition for occurrence of homoclinic chaos is always satisfied. A perturbation is added to the system to control the chaos obtained. Constraints on the parameters of the new system, at which homoclinic chaos is realized in it, are found. The attraction basins are plotted. It is found that their structure is fractal when the damping parameter values are less than the critical ones obtained by the Melnikov approach. The results of the numerical analysis go in agreement with those acquired theoretically.
Только метаданные
Suppression of chaos in the periodically perturbed generalized complex Ginzburg–Landau equation by means of parametric excitation
(2023) Lavrova, S.; Kudryashov, N.; Лаврова, София Федоровна; Кудряшов, Николай Алексеевич