Персона: 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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- ПубликацияОткрытый доступOn some properties of the coupled Fitzhugh-Nagumo equations(2019) Lavrova, S. F.; Kudryashov, N. A.; Sinelshchikov, D. I.; Лаврова, София Федоровна; Кудряшов, Николай Алексеевич© 2019 Published under licence by IOP Publishing Ltd.We consider the FitzHugh-Nagumo model describing two neurons electrically coupled via ion flow through gap juctions between them. This model is a simple example of a neural network, which has a vast amount of periodic behaviors. It is shown that system of equations describing this model does not pass the Painlevé test. Analysis of stability of system's trivial stationary point is carried out. It is shown that this equilibrium point is not always stable. For some parameter regions where solution oscillates bifurcation diagrams are plotted and Lyapunov exponents are calculated. It is shown that analyzed non-stationary solutions are quasiperiodic.
- ПубликацияТолько метаданныеProperties 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 ФедоровнаThe Chavy-Waddy–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-Waddy–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.
- ПубликацияТолько метаданныеTraveling wave solutions of the derivative nonlinear Schrodinger hierarchy(2024) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна
- ПубликацияОткрытый доступPainleve Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrodinger Equation(2024) Kudryashov, N. A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София ФедоровнаThe second partial differential equation from the Kaupў??Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevѓ? test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrѓ?dinger equations and may be used for the description of optical solitons in a nonlinear medium.
- ПубликацияОткрытый доступAnalytical solutions and conservation laws of the generalized model for propagation pulses with four powers of nonlinearity(2024) Kudryashov, N. A.; Lavrova, S. F.; Nifontov, D. R.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна; Нифонтов, Даниил РомановичAnalytical solutions of the generalized nonlinear Schrѓ?dinger with four powers of nonlinearity for description of propagating pulses in optical fiber are presented. Optical solitons corresponding to the mathematical model are given. Conservation laws of the generalized model for propagation pulses with four powers of nonlinearity are written. To the best of our knowledge, the conservation laws obtained have not yet been presented in literature. The equation investigated generalizes several well-known models, which allows us to evaluate the influence of various processes on pulse propagation. Conservative quantities for the bright optical soliton, corresponding to its power, momentum and energy, are calculated. The analytical expressions for conservative quantities obtained can be applied to check whether numerical schemes for the explored equation are conservative.
- ПубликацияТолько метаданныеDynamical 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.
- ПубликацияТолько метаданныеDynamical 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.
- ПубликацияТолько метаданныеComplex 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.
- ПубликацияТолько метаданныеNonlinear 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.
- ПубликацияТолько метаданныеOn 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.