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.
- 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.
- ПубликацияОткрытый доступBifurcations of Phase Portraits, Exact Solutions and Conservation Laws of the Generalized Gerdjikov–Ivanov Model(2023) Kudryashov, N. A.; Lavrova, S. F.; Nifontov, D. R.; Кудряшов, Николай Алексеевич; Лаврова, София Федоровна; Нифонтов, Даниил РомановичThis article explores the generalized Gerdjikov–Ivanov equation describing the propagation of pulses in optical fiber. The equation studied has a variety of applications, for instance, in photonic crystal fibers. In contrast to the classical Gerdjikov–Ivanov equation, the solution of the Cauchy problem for the studied equation cannot be found by the inverse scattering problem method. In this regard, analytical solutions for the generalized Gerdjikov–Ivanov equation are found using traveling-wave variables. Phase portraits of an ordinary differential equation corresponding to the partial differential equation under consideration are constructed. Three conservation laws for the generalized equation corresponding to power conservation, moment and energy are found by the method of direct transformations. Conservative densities corresponding to optical solitons of the generalized Gerdjikov–Ivanov equation are provided. The conservative quantities obtained have not been presented before in the literature, to the best of our knowledge.
- ПубликацияОткрытый доступPainleve Test, Phase Plane Analysis and Analytical Solutions of the Chavy-Waddy-Kolokolnikov Model for the Description of Bacterial Colonies(2023) Kudryashov, N.A.; Lavrova, S. F.; Кудряшов, Николай Алексеевич; Лаврова, София ФедоровнаThe Chavy-Waddy-Kolokolnikov model for the description of bacterial colonies is considered. In order to establish if the mathematical model is integrable, the Painleve test is conducted for the nonlinear ordinary differential equation which corresponds to the fourth-order partial differential equation. The restrictions on the mathematical model parameters for ordinary differential equations to pass the Painleve test are obtained. It is determined that the method of the inverse scattering transform does not solve the Cauchy problem for the original mathematical model, since the corresponding nonlinear ordinary differential equation passes the Painleve test only when its solution is stationary. In the case of the stationary solution, the first integral of the equation is obtained, which makes it possible to represent the general solution in the quadrature form. The stability of the stationary points of the investigated mathematical model is carried out and their classification is proposed. Periodic and solitary stationary solutions of the Chavy-Waddy-Kolokolnikov model are constructed for various parameter values. To build analytical solutions, the method of the simplest equations is also used. The solutions, obtained in the form of a truncated expansion in powers of the logistic function, are represented as a closed formula using the formula for the Newton binomial.