Персона: Сафонова, Дарья Владимировна
Загружается...
Email Address
Birth Date
Научные группы
Организационные подразделения
Организационная единица
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.
Статус
Фамилия
Сафонова
Имя
Дарья Владимировна
Имя
6 results
Результаты поиска
Теперь показываю 1 - 6 из 6
- ПубликацияТолько метаданныеPainleve analysis and traveling wave solutions of the sixth order differential equation with non-local nonlinearity(2021) Kudryashov, N. A.; Safonova, D. V.; Кудряшов, Николай Алексеевич; Сафонова, Дарья Владимировна© 2021 Elsevier GmbHIn this paper, we study a nonlinear partial differential equation for describing high dispersion optical soliton with non-local nonlinearity. Taking into account the traveling wave reduction, we get system of ordinary differential equations (ODEs) for real and imaginary parts of the original equation. To determine the integrability of equation we apply the Painlevé test for analysis of obtained ODE system. We illustrate that the system of equations does not have the Painlevé property since there is only one integer Fuchs index. However using the Painlevé data we find the compatibility conditions for the ODE system. Under these conditions, the traveling wave solution of nonlinear differential equations are constructed and illustrated.
- ПубликацияТолько метаданныеNonautonomous first integrals and general solutions of the KdV-Burgers and mKdV-Burgers equations with the source(2019) Kudryashov, N. A.; Safonova, D. V.; Кудряшов, Николай Алексеевич; Сафонова, Дарья Владимировна© 2019 John Wiley & Sons, Ltd.The method for constructing first integrals and general solutions of nonlinear ordinary differential equations is presented. The method is based on index accounting of the Fuchs indices, which appeared during the Painlevé test of a nonlinear differential equation. The Fuchs indices indicate us the leading members of the first integrals for the origin differential equation. Taking into account the values of the Fuchs indices, we can construct the auxiliary equation, which allows to look for the first integrals of nonlinear differential equations. The method is used to obtain the first integrals and general solutions of the KdV-Burgers and the mKdV-Burgers equations with a source. The nonautonomous first integrals in the polynomials form are found. The general solutions of these nonlinear differential equations under at some additional conditions on the parameters of differential equations are also obtained. Illustrations of some solutions of the KdV-Burgers and the mKdV-Burgers are given.
- ПубликацияТолько метаданныеPainleve Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan — Kundu — Lakshmanan Equation(2019) Kudryashov, N. A.; Safonova, D. V.; Biswas, A.; Кудряшов, Николай Алексеевич; Сафонова, Дарья Владимировна© 2019, Pleiades Publishing, Ltd.This paper considers the Radhakrishnan — Kundu — Laksmanan (RKL) equation to analyze dispersive nonlinear waves in polarization-preserving fibers. The Cauchy problem for this equation cannot be solved by the inverse scattering transform (IST) and we look for exact solutions of this equation using the traveling wave reduction. The Painlevé analysis for the traveling wave reduction of the RKL equation is discussed. A first integral of traveling wave reduction for the RKL equation is recovered. Using this first integral, we secure a general solution along with additional conditions on the parameters of the mathematical model. The final solution is expressed in terms of the Weierstrass elliptic function. Periodic and solitary wave solutions of the RKL equation in the form of the traveling wave reduction are presented and illustrated.
- ПубликацияТолько метаданныеPainleve analysis and traveling wave solutions of the fourth-order differential equation for pulse with non-local nonlinearity(2021) Kudryashov, N. A.; Safonova, D. V.; Кудряшов, Николай Алексеевич; Сафонова, Дарья Владимировна© 2020 Elsevier GmbHNonlinear fourth-order partial differential equation with non-local nonlinearity for describing pulses in optical fiber is considered. The traveling wave reductions to the equation are used to obtain the real and imaginary parts of nonlinear differential equation. Using the Painlevé analysis to the system of equations it is shown that this system does not have the general solution with four arbitrary constants. However the equation can have exact solution with the smaller number of arbitrary constants. Conditions for some parameters of the mathematical model are found for solution of the system of equations. Exact solutions for the system of equations are found by the means of the simplest equation method. Exact solutions are given using the Jacobi elliptic functions.
- ПубликацияТолько метаданныеPainleve Analysis and Exact Solution to The Traveling Wave Reduction of Nonlinear Differential Equations for Describing Pulse in Optical Fiber(2022) Kudryashov, N. A.; Safonova, D. V.; Кудряшов, Николай Алексеевич; Сафонова, Дарья Владимировна© 2022 American Institute of Physics Inc.. All rights reserved.Two high-order nonlinear partial differential equations are considered. They are used for describing propagation pulses in optical fibers. The Painlevé analysis for traveling wave reduction of the equations is completed. As a result of Painlevé test the condition on some parameters of the models are obtained. For constructing the exact solution, simplest equations method is used. Periodic and solitary wave solutions are found.
- 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.