Analytical properties of nonlinear dislocation equation

Kudryashov, Nikolay A.

doi:10.1016/j.aml.2017.01.015

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…Substituting equation (11) into equation (10) leads to where C 1 is the arbitrary constant of integration. The solution of equation ( 13) can be constructed by means of the modern methods suggested in recent years to look for exact solutions of non-integrable differential equations [23][24][25][26][27][28][29][30][31][32][33]. Taking these methods into consideration we can search for some exact solutions of equation (13).…”

Section: Cnoidal and Solitary Waves For Polarization Fieldmentioning

confidence: 99%

Solitons in thin-film ferroelectric material

et al. 2018

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Through the Landau-Ginzburg-Devonshire mean field theory, the equation governing the behavior of the polarization field in ferroelectric material is derived. Ferroelectric material is subjected to a standing electric field which inhibits remanent polarization and facilitates the access to the instantaneous polarization. Some transformations turn the equation into a well-known ordinary differential equation. As a result, dark soliton and cnoidal waves, which have not yet been observed in ferroelectrics, are obtained. Also, a bright soliton is found. It exists in a given range of temperatures and has an amplitude and a width which vary inversely with temperature.

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Section: Cnoidal and Solitary Waves For Polarization Fieldmentioning

confidence: 99%

Solitons in thin-film ferroelectric material

et al. 2018

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“…Здесь τ = ε 2 t -медленное время, зависимость от второго и третьего аргументов функций u j (τ, t, x) является периодической. Еще раз отметим, что ряды вида (16) являются формальными, т. е. вопрос об их сходимости не рассматривается. Из результатов приводимых ниже утверждений следует, что они -асимптотические.…”

Section: регулярные решенияunclassified

“…Используя методы работ [10]- [14], ниже мы строим семейства специальных краевых задач для описания различных групп решений исходной краевой задачи (3), (4). Отметим, что особо важным с прикладной точки зрения [1], [15], [16] является случай, когда параметр a мал. В связи с этим в разделе 2 мы рассматриваем случай, когда a 0 = 0, т. е.…”

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Regular and irregular solutions in the problem of dislocations in solids

Kashchenko¹

2018

TMF

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Рассмотрены асимптотические по невязке решения исходного дифференциального уравнения с отклонениями пространственной переменной. Все решения естественным образом разбиваются на классы, регулярно и нерегулярно зависящие от параметров задачи. В различных областях из малой окрестности нулевого состояния равновесия фазового пространства построены специальные нелинейные распределенные уравнения и системы уравнений, зависящие от континуальных семейств некоторых параметров. В частности, показано, что решения исходного пространственного одномерного уравнения можно описать решениями специальных уравнений и систем уравнений шредингеровского типа в пространственно двумерной области изменения аргументов.

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“…Many physical processes such as nonlinear optics, electromagnetism, plasma, shallow water wave propagation, fluid dynamics and many more can be represented using nonlinear partial differential equations [6][7][8][9]. There are many efficient and compelling methods that have been made to extract the solution of these equations in recent years [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables

2021

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The objective of this research is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov-Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as collective variables (CVs). This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge-Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated it illustrated it graphically. Furthermore, Figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

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Analytical properties of nonlinear dislocation equation

Cited by 10 publications

References 13 publications

Solitons in thin-film ferroelectric material

Solitons in thin-film ferroelectric material

Regular and irregular solutions in the problem of dislocations in solids

Novel optical solitons to the perturbed Gerdjikov–Ivanov equation via collective variables

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