Wen-shan Duan

Ion-acoustic solitary waves and their interaction in a weakly relativistic two- dimensional thermal plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a weakly relativistic two-dimensional thermal plasma. Two Korteweg–de Vries equations for small but finite amplitude solitary waves in both ξ and η directions are derived. The phase shifts and trajectories of two solitary waves after the collision with an arbitrary angle α are also obtained. The effects of parameters of the normalized ion temperature σ, the ratio of heat capacity δ, the relativistic factor Fγ, and the colliding angle α on the amplitudes, the widths and the phase shifts of both the colliding solitary waves are studied. The effects of these parameters on the new nonlinear wave created by the collision between two solitary waves are examined as well. The results suggest that these parameters can significantly influence the amplitude, the width of the newly formed nonlinear wave and the colliding solitary waves. The phase shifts of the colliding solitary waves strongly depend on the colliding angle α. M...

Weakly two-dimensional dust acoustic waves

For dust acoustic waves in unmagnetized plasma comprising cold dust grains and both isothermal electrons and ions, small but finite amplitude nonlinear waves are governed by the Korteweg–de Vries equation. The weakly transverse long wavelength perturbations for nonlinear dust acoustic waves are investigated in this paper. It has been shown that the governing equation for this process is the Kadomtsev–Petviashvili equation. It suggests that the transverse perturbations for the nonlinear acoustic solitary waves in a dusty plasma are stable.

Collisional phase shifts between two colliding solitary waves in a three-dimensional magnetized dusty plasma

Interaction of dust acoustic solitary waves in two different directions in a three-dimensional dusty plasma is investigated. The phase shifts after collision of two solitary waves with arbitrary angle in a three-dimensional magnetized dusty plasma are studied. By using the extended Poincare–Lighthill–Kuo perturbation method, two Korteweg–de Vries equations for nonlinear waves in both ξ and η directions are obtained. The effects of the collision angle θ, the ratio of dust temperature to ion temperature σ, the ratio of ion temperature to electron temperature β, the ratio of effective temperature to ion temperature s, and the ratio of the number densities of both ion and electron to the density of dust particles μ and ν on the phase shifts are discussed.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev–Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Korteweg-de Vries solitons in inhomogeneous plasma

Transmission and reflection of a soliton in an inhomogeneous plasma are investigated. Both the transmission and the reflection can be described by the KdV (Korteweg-de Vries) equations for the discontinuous case. The numbers and magnitudes for transmitted and reflected solitons are analytically given. The transmission can be described by the KdV-type equation for continuous varying inhomogeneous plasma, and the quasi-solitons is also analytically given.

Waves in two-dimensional hexagonal crystal

Two-dimensional hexagonal crystal is investigated in this paper. The dispersion relations for both compressional and transverse waves in different directions are studied as well. The analytical results are in agreement with the experimental ones reported previously. The small amplitude but finite long wavelength nonlinear waves propagating in the hexagonal crystal are also investigated. This investigation indicates that the solitary waves propagating in the directions of either n or m are stable.

Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.

Effects of dust size distribution on dust acoustic waves in magnetized two-ion-temperature dusty plasmas

A Zakharov–Kuznetsov (ZK) equation, a modified ZK (mZK) equation, and a coupled ZK (cZK) equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been investigated in this paper. The variations of the linear dispersion relation and group velocity, nonlinear solitary wave amplitude, and width with an arbitrary dust size distribution function are studied numerically. We conclude that they all increase as the total number density of dust grains increases, and they are greater for unusual dusty plasma (the number density of larger dust grains is greater than that of smaller dust grains) than that of usual dusty plasma (the number density of smaller dust grains is greater than that of larger dust grains). It is noted that the frequency of the linear wave increases as the wave number along the magnetic direction increases. Furthermore, the width of the nonlinear waves increases but its amplitude decreases as the wave number alo...

Rectification and phase locking in overdamped two-dimensional Frenkel-Kontorova model

The rectification phenomena and the phase locking for an overdamped two-dimensional Frenkel-Kontorova model system with commensurate structure under ac- and dc-driven external forces are demonstrated. As a function of longitudinal dc amplitude, the longitudinal velocity increases in a series of steps of height jν0. In the steps, rectifications in the transverse direction occur though there are no net dc force in the transverse direction. Our results can be applied to vortices in superconductors, classical electron motion, biomolecules moving through 2D arrays of posts, and especially in tribology. In these active ratchets the rectified velocities can be controlled by jν0.

The effect of dust size distribution on envelope wave packet in magnetized two-temperature-ion dusty plasma

The effect of arbitrary dust size distribution on a nonlinear envelope wave packet in a magnetized two-temperature-ion dusty plasma has been studied in this paper. By using the reductive perturbation method, the dispersion relation and a (3+1)-dimensional nonlinear Schrodinger equation (NLSE) have been obtained. It is found that the frequency, the group velocity, and the propagation behavior of the envelope waves have been significantly influenced by different dust size distributions. It is also found that the frequency increases as the total number density of dust particles increases. Moreover, it seems that the frequency for usual dusty plasma is smaller than that of the unusual case. On the other hand, the modulational instability of envelope waves has also been discussed by analyzing the solution of the NLSE. It is shown that the conditions of modulational instability for envelope waves are different for various cases.