Dynamic behavior of the (3+1)-dimensional generalized Johnson model in a dusty plasma

In this paper, we study the (3+1)-dimensional generalized Johnson model, which can be used to describe the dust-ion-acoustic waves in a cosmic unmagnetized dusty plasma, and its perturbed model, which can be found in an unmagnetized dusty plasma for the electron temperature below the Curie temperature. (I) For the original model: Bilinear form and soliton solutions are obtained. Amplitude of the one soliton reaches the maximum when the equilibrium electron (ne0) and ion (ni0) densities take certain values which correspond withne0/ni0= 2. Overtaking and head-on interactions between the two solitons are given. (II) For the perturbed model: Phase projections are given numerically. Via the spectral analysis, two kinds of chaotic motions, i.e., the weak and developed chaos, are investigated. Largest Lyapunov exponents and power spectra are investigated to corroborate that those motions are indeed chaotic. Dynamic behavior of such a perturbed model varying with the external perturbation is different when the nonlinear term changes. With the damped term considered, two kinds of periodic motions are studied, and spectra of those periodic motions are also given. Through the comparison between the chaotic motions and periodic ones, possible chaotic or periodic motions in the perturbed model can be predicted.

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On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

GUB Journal of Science and Engineering ◽

10.3329/gubjse.v5i1.47898 ◽

2018 ◽

Vol 5 (1) ◽

pp. 31-36

Author(s):

Md Monirul Islam ◽

Muztuba Ahbab ◽

Md Robiul Islam ◽

Md Humayun Kabir

Keyword(s):

Solitary Wave ◽

Acoustic Waves ◽

Water Waves ◽

Wave Equations ◽

Rectangular Channel ◽

Soliton Solutions ◽

Boussinesq Equations ◽

Travelling Wave ◽

Ion Acoustic Waves ◽

Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

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Nonplanar dust acoustic waves in a four-component dusty plasma with double spectral distributed electrons: modulational instability and rogue waves

Waves in Random and Complex Media ◽

10.1080/17455030.2021.1951886 ◽

2021 ◽

pp. 1-20

Author(s):

S. K. El-Labany ◽

W. F. El-Taibany ◽

A. A. El-Tantawy ◽

N. A. Zedan

Keyword(s):

Dusty Plasma ◽

Acoustic Waves ◽

Modulational Instability ◽

Rogue Waves ◽

Dust Acoustic Waves ◽

Dust Acoustic

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Nonlinear dust acoustic waves in an inhomogeneous magnetized quantum dusty plasma

Waves in Random and Complex Media ◽

10.1080/17455030.2021.1880030 ◽

2021 ◽

pp. 1-16

Author(s):

A. Atteya ◽

M. A. El-Borie ◽

G. D. Roston ◽

A. S. El-Helbawy

Keyword(s):

Dusty Plasma ◽

Acoustic Waves ◽

Dust Acoustic Waves ◽

Dust Acoustic

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Bifurcation Analysis of Self-Acting Gas Journal Bearings

Journal of Tribology ◽

10.1115/1.1388302 ◽

2001 ◽

Vol 123 (4) ◽

pp. 755-767 ◽

Cited By ~ 36

Author(s):

Cheng-Chi Wang ◽

Cha’o-Ku`ang Chen

Keyword(s):

Dynamic Behavior ◽

Reynolds Equation ◽

Rotational Velocity ◽

Power Spectra ◽

Journal Bearings ◽

Operating Conditions ◽

Finite Differences Method ◽

Subharmonic Response ◽

Rotor Center ◽

Rotor Mass

This paper studies the bifurcation of a rigid rotor supported by a gas film bearing. A time-dependent mathematical model for gas journal bearings is presented. The finite differences method and the Successive Over Relation (S.O.R) method are employed to solve the Reynolds’ equation. The system state trajectory, Poincare´ maps, power spectra, and bifurcation diagrams are used to analyze the dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions. The analysis shows how the existence of a complex dynamic behavior comprising periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in rotor mass and rotational velocity. The results of this study contribute to a further understanding of the nonlinear dynamics of gas film rotor-bearing systems.

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N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

Modern Physics Letters B ◽

10.1142/s0217984921502778 ◽

2021 ◽

pp. 2150277

Author(s):

Hongcai Ma ◽

Qiaoxin Cheng ◽

Aiping Deng

Keyword(s):

Dynamic Behavior ◽

Soliton Solution ◽

Soliton Solutions ◽

Wave Interaction ◽

Bilinear Transformation ◽

Interaction Solution ◽

Interaction Solutions ◽

Ytsf Equation ◽

Line Soliton

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

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