Ion‐Acoustic Waves Instability in a Three Components Magneto‐Plasma with Nonthermal Electrons

A theoretical investigation has been made on obliquely propagating ion‐acoustic (IA) solitary structures in a three components magneto‐plasma containing cold inertial ions, Boltzmann distributed positrons, and hot non‐thermal electrons. The Zakharov‐Kuznetsov equation has been derived by the reductive perturbation method, and its solitary wave solution has been analyzed. Multi‐dimensional instability has also studied by the small‐k (long wave‐length plane wave) perturbation expansion technique, which is found to exist in such a plasma. The effects of the external magnetic field, nonthermal electrons, obliqueness and temperature ratio have significantly modified the basic properties of small but finite‐amplitude IA solitary waves, such as amplitude, width, instability criterion and the growth rate. The present investigation contributes to the physics of the nonlinear IA waves in space and laboratory electron‐positron‐ion magneto‐plasmas in which wave damping produces an electron tail. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solitary wave for a nonintegrable discrete nonlinear Schr?dinger equation in nonlinear optical waveguide arrays

We study a nonintegrable discrete nonlinear Schr?dinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.     

A new spiky soliton and an explosive mode of the nonlinear driftwave equation

A new type of nonlinear wave modes which occurs in the electrostatic drift waves in an inhomogeneous magnetized plasma is presented. The author predicts the existence of a new type of spiky solitary wave and an explosive mode with a negative potential as stationary solutions of this equation. These solutions are a consequence of a density gradient and not connected with a temperature gradient. These new nonlinear wave solutions appear to make a step forward in the general scheme of nonlinear normal modes for plasma waves. Using these nonlinear wave modes, the author can explain the solitary structure and the explosive event concerning nonlinear drift waves propagating in space     

Coupled nonlinear Schrödinger equations including growth and damping

We give an analytical and numerical analysis of a system of coupled nonlinear Schrödinger equations with complex coefficients describing wave-wave interaction in the presence of a linear and non-linear damping (growth). An exact solitary solution is found for arbitrary damping rate for one of the waves when the linear damping of the second wave is zero. In general, the wave envelopes are composed of dispersive shock waves which are explosively unstable.     

Dust acoustic wave in a dusty plasmas with streaming ions and nonadiabatic dust charge variation

The effects of nonadiabatic dust charge fluctuation on the nonlinear propagation of the dust acoustic (DA) solitary wave in collisionless dusty plasma with streaming ions have been investigated. By using the reductive perturbation technique, a modified Korteweg-de Vries (mKdV) equation governing the nonlinear waves was derived and the solitary solution of the mKdV equation was also obtained. It was shown that the damping rate of the slow mode DA solitary wave was strongly affected by the ion streaming velocity.     

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.     

Time reversing solitary waves

We present new results for the time reversal of nonlinear pulses traveling in a random medium, in particular for solitary waves. We consider long water waves propagating in the presence of a spatially random depth. Both hyperbolic and dispersive regimes are considered. We demonstrate that in the presence of properly scaled stochastic forcing the solution to the nonlinear (shallow water) conservation law is regularized leading to a viscous shock profile. This enables time-reversal experiments beyond the critical time for shock formation. Furthermore, we present numerical experiments for the time-reversed refocusing of solitary waves in a regime where theory is not yet available. Solitary wave refocusing simulations are performed with a new Boussinesq model, both in transmission and in reflection.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

Propagation properties of dust-electron-acoustic waves in weakly magnetized dusty nonthermal plasmas

The linear and nonlinear properties of dust-electron acoustic waves (DEAWs) propagating in magnetized, collisionless, dusty plasma system containing inertial cold electrons, Maxwellian hot electrons, nonthermal ions, and arbitrarily (positively or negatively) charged stationary dust are investigated. The reductive perturbation technique is employed to reduce the basic set of fluid equations to the modified Korteweg-de Vries equation or Ostrovsky's equation, which governs the dynamics of small amplitude DEAWs in a weakly magnetized dusty nonthermal plasma. The approximate analytical as well as numerical solutions reveal that the basic characteristics of DEA nonlinear structures are found to be significantly modified by the key plasma configuration parameters. It is found that the leading compressive or rarefactive solitary wave structure separates from a trailing wave packet during a considerable time under the influence of magnetic field-induced Lorentz force.     

On reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

内孤立波沿缓坡地形传播特性的实验研究

以南中国海东北部海域底部缓坡地形为背景, 在大型重力式分层流水槽中模拟了下凹型内孤立波沿缓坡地形传播过程中的浅化、破碎、分裂等现象, 利用分层染色标识方法和多点组合探头阵列技术对内孤立波沿缓坡地形演化特征进行了定性分析和定量测量. 实验表明: 浅化效应使内孤立波传播速度减小, 对大振幅内孤立波具有抑制作用, 对小振幅波具有放大效应; 浅化效应可导致内孤立波的剪切失稳及破碎, 还可导致大振幅内孤立波的分裂. 利用Miles稳定性理论可定性描述内孤立波沿缓坡地形传播时发生不稳定状态的位置, 实验结果与理论分析相符合. 关键词： 分层流 缓坡地形 内孤立波 不稳定性     

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.     

Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.     

Rogue waves in shallow water

Most of the processes resulting in the formation of unexpectedly high surface waves in deep water (such as dispersive and geometrical focusing, interactions with currents and internal waves, reflection from caustic areas, etc.) are active also in shallow areas. Only the mechanism of modulational instability is not active in finite depth conditions. Instead, wave amplification along certain coastal profiles and the drastic dependence of the run-up height on the incident wave shape may substantially contribute to the formation of rogue waves in the nearshore. A unique source of long-living rogue waves (that has no analogues in the deep ocean) is the nonlinear interaction of obliquely propagating solitary shallow-water waves and an equivalent mechanism of Mach reflection of waves from the coast. The characteristic features of these processes are (i) extreme amplification of the steepness of the wave fronts, (ii) change in the orientation of the largest wave crests compared with that of the counterparts and (iii) rapid displacement of the location of the extreme wave humps along the crests of the interacting waves. The presence of coasts raises a number of related questions such as the possibility of conversion of rogue waves into sneaker waves with extremely high run-up. Also, the reaction of bottom sediments and the entire coastal zone to the rogue waves may be drastic.     

A Second-Order Theory for Electron Plasma Solitary Waves in a Cylindrical Waveguide

To describe the long time asymptotic behaviour of weakly nonlinear plasma waves propagating in a strongly magnetized plasmafilled cylindrical waveguide the usual KDV equation which is first order in wave amplitude is extended to second order including the effects of finite temperature, mobile ions and giving a proper treatment to the radial co-ordinate for all possible modes of propagation. The second-order effects on the first-order solitary wave profile, phase speed and first order correction to the wavelength are all determined and discussed.     

Effect of excavated trapped electron distributions on ion-acoustic solitary structures in an electron-positron-ion plasma

Fully nonlinear propagation of ion-acoustic solitary waves in an unmagnetized electron-positron-ion plasma is investigated. A more realistic situation is considered in which electrons interact with the wave potential during its evolution and, follow the vortex-like excavated trapped distribution. The basic properties of large amplitude solitary waves are studied by deriving an energy integral equation involving Sagdeev potential. It is shown that effects of such electron behavior and positron concentration change the maximum values of the Mach number and amplitude for which solitary waves can exist. The small amplitude limit is also investigated by expanding the Sagdeev potential to include third-order nonlinearity of electric potential. In this case, exact analytical solution is obtained which is related to the contribution of the resonant electron to the electron density. It is shown from both highly and weakly nonlinear analysis that the plasma system under consideration supports only compressive solitary waves.     

Emission of radiation from a long Josephson junction in a thin film

Space-time nonlocal electrodynamic equations are derived for nonlinear vortex states of a Josephson junction in a film of thickness much smaller than the London penetration depth. The spectrum and damping of generalized Swihart waves propagating in such a junction are analyzed. The radiation damping constant associated with the possible emission of electromagnetic radiation is determined in the range of Swihart wave phase velocities exceeding the speed of light. The emission of radiation from nonlinear states having dimensions greater than the distance traversed by light in vacuum during the characteristic time of variation of the phase difference is investigated. It is shown that the flux density of radiation emitted by such states is localized in a plane orthogonal to the axis of the tunnel junction and depends weakly on the angle of observation in this plane. Zh. éksp. Teor. Fiz. 115, 1426–1449 (April 1999)     

Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to finite difference methods

The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems. Features that a computational model must have, to capture large scale realistic effects (for over the horizon or “OTH” radar communication, for example), include propagation of short waves with scattering and partial absorption by complex topography. For these reasons, it is not feasible to use Green’s Function or any simple integral method, which neglects these intermediate effects and requires a known propagation function between source and observer. In this paper, we describe a new method for propagating such short waves over long distances, including intersecting scattered waves. The new method appears to be much simpler than conventional high frequency schemes: Lagrangian “particle” based approaches, such as “ray tracing” become very complex in 3-D, especially for waves that may be expanding, or even intersecting. The other high frequency scheme in common use, the Eikonal, also has difficulty with intersecting waves.Our approach, based on nonlinear solitary waves concentrated about centroid surfaces of physical wave features, is related to that of Whitham [1], which involves solving wave fronts propagating on characteristics. Then, the evolving electromagnetic (or acoustic) field can be approximated as a collection of propagating co-dimension one surfaces (for example, 2-D surfaces in three dimensions). This approach involves solving propagation equations discretely on an Eulerian grid to approximate the linear wave equation. However, to propagate short waves over long distances, conventional Eulerian numerical methods, which attempt to resolve the structure of each wave, require far too many grid cells and are not feasible on current or foreseeable computers. Instead, we employ an “extended” wave equation that captures the important features of the propagating waves. This method is first formulated at the partial differential equation (PDE) level, as a wave equation with an added “confining” term that involves both a positive and a negative dissipation. Once we have the stable PDE, the discrete formulation is simply a multidimensional PDE with (stable) perturbations caused by the discretization. The resulting discrete solution can then be low order and very simple and yet remain stable over arbitrarily long times. When discretized and solved on an Eulerian grid, this new method allows far coarser grids than required by conventional resolution considerations, while still accounting for the effects of varying atmospheric and topographic features. An important point is that the new method is in the same form as conventional discrete wave equation methods. However, the conventional solution eventually decays, and only the “intermediate asymptotic” solution can be used. Simply by adding an extra term, we show that a nontrivial true asymptotic solution can be obtained. A similar solitary wave based approach has been used successfully in a different problem (involving “Vorticity Confinement”), for a number of years.     

Nonlinear propagation of fast and slow magnetosonic waves in collisional plasmas

Low-frequency fast and slow magnetosonic waves propagating in electron ion plasmas with damping effects through ions and neutral atoms collisions are investigated. Linear wave analysis is performed to obtain dispersion relation. The reductive perturbation method is applied and it is shown that fast and slow modes of nonlinear magnetosonic wave are governed by damped Korteweg-de Vries (DKdV) equation in the presence of ion neutral collisions in plasmas. The analytical solution of DKdV soliton is presented under the assumption of weak collisional effects and numerical solutions of DKdV equation are also obtained using two-level finite difference scheme with the help of Runge–Kutta method at different plasma parameters. The damping of nonlinear fast and slow magnetosonic wave structures at different times are discussed in the context of space plasma situations where ions and neutral atoms collisions exist.     

Modulation of dust acoustic waves with non-adiabatic dust charge fluctuations

The modulational instability of dust acoustic waves in a dusty plasma with non-adiabatic dust charge fluctuation is studied. Using the perturbation method, a modified nonlinear Schrödinger equation containing a damping term that comes from the effect of dust charge variation is derived. It is found that the modulational instability of the wave packet and the propagation characters of the envelope solitary waves are modified significantly by the non-adiabatic dust charge fluctuation.