Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.     

Propagation of solitary waves in relativistic plasmas

By applying a reductive perturbation technique to the basic system of equations governing the plasma dynamics, a modified Korteweg-de Vries (K-dV) equation has been derived in relativistic plasma that includes cold ions and warm nonisothermal electrons. By reducing the effect of nonisothermality, the authors demonstrate the modification of the K-dV equation into different forms which show how to link the behavior of ion-acoustic waves in nonisothermal plasmas with that in isothermal plasmas     

From bell-shaped solitary wave to W/M-shaped solitary wave solutions in an integrable nonlinear wave equation

The bifurcation theory of dynamical systems is applied to an integrable nonlinear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.     

Stability of solitary wave trains in Hamiltonian wave systems

A class of Hamiltonian nonlinear wave equations possessing complex solitary waves with exponential decay is studied. It is shown that the interpulse interactions in a train of nearly identical solitary waves with large separations between the individual solitary waves are approximately described by a double Toda lattice system, with two variables at each lattice site. Under certain conditions, which are explicitly identified as Cauchy-Riemann equations, the two dynamical variables are real and imaginary parts of a single complex variable, leading to the complex Toda lattice equations, which is a discrete integrable dynamical system. This analysis generalizes to certain nonintegrable partial differential equations a recent result for the nonlinear Schr?dinger equation, and is important for the study of nonlinear communications channels in optical fibers. An example, the cubic-quintic nonlinear Schr?dinger equation, is worked out in detail to show that the theory can be carried through analytically. The theory is used to determine the stability of an infinite chain of nearly identical pulses separated by large time intervals. The entire theory is nonperturbative in the sense that the nonlinear wave equation need not be a weak perturbation of an integrable one.     

Travelling solitary wave solutions to a compound KdV-Burgers equation

Explicit travelling solitary wave solutions to a compound KdV-Burgers equation are obtained by using an automated method. A two-dimensional generalization is discussed.     

Maturing process of solitary wave train in a step-down chain

In a step-down chain a solitary wave (SW) evolves into an SW train (SWT), but the formation of well-defined SWT takes time and space and little is known of the process from immature into mature SWT. We therefore perform a detailed numerical study of this process by analysing the local velocity amplitude and peak overlap of immature ordered SWs. The first SW continuously increases to maximal velocity amplitude and peak overlap until it is matured, but for following SWs there exist a minimal and maximal value of local velocity amplitude and, a minimal and maximal value of local peak overlap, clarifying the details of the energy propagation along the stepped chain. The immature and mature SWTs show the same dependence of the phase velocity on the SWs sequence. These provide guidelines for when or where the attention should be paid in the study of SWT.     

Propagation of a Gaussian-beam wave through a random phase screen

Tractable analytic expressions are developed for a variety of basic statistical quantities involving a Gaussian-beam wave propagating through a random medium confined to a portion of the propagation path between input and output planes, the limiting case of which defines a thin random phase screen. For a plane wave incident on a phase screen located midway between input and output planes, it is well known that the statistics in the receiver plane are in close agreement with those associated with a plane wave propagating through an extended random medium between input and output planes. For a similar comparison between a phase screen and extended turbulence in the case of a Gaussian-beam wave at the input plane, the present analysis reveals that the phase screen must be positioned between input and output planes differently from the plane-wave case, the position being dependent upon the Fresnel ratio of the Gaussian beam. The analytic results developed in this paper for the thin phase screen model are based on the Kolmogorov power-law spectrum for refractive-index fluctuations and the Rytov approximation. Extension of these results to multiple phase screens is also discussed.     

Propagation of terahertz waves in a dust acoustic wave

The propagation of terahertz waves in a dust acoustic wave is investigated numerically. By assuming a sinus profile of the dust number density in the dust acoustic waves, the transmission properties are calculated using finite difference time domain method. It shows that the dust acoustic wave can function similarly as a Bragg filter to block the terahertz waves of a certain wavelength. The bandwidth of the filter depends on the density profile of the dust acoustic wave.     

有损金属圆波导中电磁波传输特性的研究

基于电磁模式的色散方程，研究了有损金属圆波导中电磁模式的传输问题.在考虑了损耗层厚度影响的情况下，得到了各模式传输常数的近似解析表达式，此式适用于截止频率附近.通过解析表达式和波导模式色散方程，对衰减常数和相位常数进行了大量数值计算，得到了它们随损耗层厚度、频率以及损耗层电导率的变化规律，两种方法所获得的结果有较好的一致性.研究表明，损耗强度和损耗层厚度的变化会改变波导中电磁模式的色散和简并特性，对于改善高功率回旋行波放大器中注波互作用带宽和模式竞争非常有益. 关键词： 有损圆波导 相位常数 衰减常数 色散方程     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

Newton-conjugate-gradient methods for solitary wave computations

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugate-gradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the linearization operator is non-self-adjoint, the preconditioned biconjugate-gradient method is proposed to solve the linear equation. The resulting methods are applied to compute both the ground states and excited states in a large number of physical systems such as the two-dimensional NLS equations with and without periodic potentials, the fifth-order KdV equation, and the fifth-order KP equation. Numerical results show that these proposed methods are faster than the other leading numerical methods, often by orders of magnitude. In addition, these methods are very robust and always converge in all the examples being tested. Furthermore, they are very easy to implement. It is also shown that the nonlinear conjugate gradient methods are not robust and inferior to the proposed methods.     

Interaction between solitary wave solutions to a double sine-Gordon equation

Solitary wave solutions to a double sine-Gordon equation are examined by means of numerical computations. Quasi-solitons as well as solitary wave solutions are found. The break up of initial shapes is examined.     

A double optical solitary wave in a nonlinear Schroedinger-type equation

A qualitative analysis method to efficiently solve the shallow wave equations is improved, so that a more complicated nonlinear Schr6dinger equation can be considered. By using the detailed study, some quite strange optical solitary waves are obtained in which the bright and dark optical solitary waves are allowed to coexist.     

Propagation of solitary waves in channels of decreasing depth

The changes which occur in a right-going solitary wave as it travels a channel of decreasing depth are discussed. In addition to the changes in the solitary wave, we have found through a judicious use of the conservation laws two secondary structures (a shelf and a reflection). Each of these structures is small with respect to the solitary wave, though the mass flux associated with each is of the same order as that of the solitary wave. Of interest is that the amplitude of the reflected wave does not satisfy Green's law. But rather, the amplitude of the reflected wave is constant along left-going characteristics. This finding allows us to satisfy the mass flux conservation laws to leading order and establishes the perturbed Korteweg-deVries equation as a consistent approximation for the right-going profile.     

Normal modes in a solitary wave solution to a double sine-Gordon equation

In a double sine-Gordon system the internal oscillations of a solitary wave solution can be viewed as normal modes in a number of sine-Gordon 2π-kinks and the ratio between the frequencies can be predicted. For three 2π-kinks this ration is √3.     

Multistable structure in a Korteweg-de Vries system driven by a solitary wave

The dynamical behavior of a Korteweg-de Vries (KdV) system driven by a solitary wave is studied. A hierarchy of hystereses, i.e. multistability, for the steady wave momenta is found in the system. Winding number bifurcation occurs for the steady wave solution on every hysteresis.     

Propagation of solitary ion acoustic waves in inhomogeneous plasmas

A WKB solution for the propagation of a solitary ion acoustic wave in a plasma with a density gradient is obtained.