Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Tao, Bo

doi:10.1155/2017/9312681

Cited by 4 publications

(3 citation statements)

References 42 publications

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“…This is consistent with the theory that as it is the second order formal expansion solution, the order of accuracy is 2 in the time-scale 1. As final remarks, knowing the accuracy of the formal expansion method, we could extend the application of this method to solve other mathematical engineering problems, such as those studied by researchers in [16][17][18][19][20][21][22][23][24][25][26]. Possible other problems to be solved using the formal expansion method could be those in [27][28][29][30][31][32][33][34][35][36][37].…”

Section: Simulation For the Validity Of Order Of Accuracymentioning

confidence: 98%

Formal expansion method for solving an electrical circuit model

Tjendro

Mungkasi

2019

TELKOMNIKA

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We investigate the validity of the formal expansion method for solving a second order ordinary differential equation raised from an electrical circuit problem. The formal expansion method approximates the exact solution using a series of solutions. An approximate formal expansion solution is a truncated version of this series. In this paper, we confirm using simulations that the approximate formal expansion solution is valid for a specific interval of domain of the free variable. The accuracy of the formal expansion approximation is guaranteed on the time-scale 1.

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Section: Simulation For the Validity Of Order Of Accuracymentioning

confidence: 98%

Formal expansion method for solving an electrical circuit model

Tjendro

Mungkasi

2019

TELKOMNIKA

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“…Иными словами, определим, какой должна быть функция U , чтобы уравнения ( 18) и ( 19) были совместны. В первую очередь продифференцируем уравнение (19) по x и подставим получившееся соотношение в (18). Получим…”

Section: интегрируемость модельного уравненияunclassified

Интегрируемая Модель Взаимодействия Встречных Слабонелинейных Волн На Границе Жидкости В Горизонтальном Электрическом Поле

Зубарев¹,

Кочурин²,

Kochurin

2020

TMF

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Рассмотрена нелинейная динамика свободной поверхности диэлектрической жидкости с высокой проницаемостью, находящейся в сильном горизонтальном электрическом поле. В рамках слабонелинейного приближения, когда углы наклона границы считаются малыми и в уравнениях движения учитываются лишь квадратично нелинейные по параметру малости слагаемые, получено компактное модельное уравнение для описания нелинейных волновых процессов в системе. С его использованием аналитически и численно исследовано взаимодействие распространяющихся в противоположных направлениях уединенных поверхностных волн. В частности, продемонстрировано, что встречные волны после взаимодействия восстанавливают свою форму, приобретая при этом некоторый сдвиг фаз. Установлено, что эти свойства модели обусловлены ее интегрируемостью.

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“…The KdV equation describes nonlinear waves in the long-wave region of the spectrum, that is, where the length of surface perturbations is significantly greater than the depth of the fluid [17]. Various modifications of the NLS and KdV equations were used to describe the surface electrohydrodynamic waves, for example, see the works [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics of the Interface between Dielectric Liquids at the Regime of Stabilized Kelvin-Helmholtz Instability by a Tangential Electric Field

Kochurin

Зубарев

2021

Fluids

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The nonlinear dynamics of the interface between two immiscible dielectric liquids at the regime of suppressed Kelvin-Helmholtz instability by external horizontal electric field is studied theoretically. The initial equations of the fluids motion are reduced to a single weakly nonlinear integro-differential equation that describes the interaction of solitary waves (rational solitons) propagating along the interface. The dynamics of two interacting solitons is regular and integrable; they can combine into a stable wave packet (breather). It is shown that the interaction of three solitons becomes complex and, for a wide rang of initial conditions, chaotic. The numerically obtained Poincaré sections demonstrate the destruction of toroidal trajectories in the phase space during the transition of the system to a chaotic regime of fluid motion. Such a behaviour is consistent with the Kolmogorov-Arnold-Moser theory describing quasi-periodic chaotic motion in Hamiltonian systems. At the developed chaotic state, the system fast loses the information on its initial state; the corresponding estimate for Lyapunov exponent is obtained. From the physical point of view, the chaotic behavior of the system is related with structural instability of the soliton triplet. The triplet can decay into a solitary wave and stable breather consisting of two interacting solitons.

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Model Equations for Three-Dimensional Nonlinear Water Waves under Tangential Electric Field

Cited by 4 publications

References 42 publications

Formal expansion method for solving an electrical circuit model

Formal expansion method for solving an electrical circuit model

Интегрируемая Модель Взаимодействия Встречных Слабонелинейных Волн На Границе Жидкости В Горизонтальном Электрическом Поле

Chaotic Dynamics of the Interface between Dielectric Liquids at the Regime of Stabilized Kelvin-Helmholtz Instability by a Tangential Electric Field

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