Electrostatic solitary waves associated with relativistic nonextensive electrons in magnetized fusion plasma

Properties of nonlinear electrostatic solitary waves in a magnetized multicomponent system of plasma containing of warm fluid ions, weakly relativistic warm fluid electrons and q-nonextensive distributed electrons using reductive perturbation method, have been surveyed. For this purpose, a KdV soliton type solution has been employed. The dependence of solitary wave structure, solitary wave maximum amplitude, and phase velocity of soliton on the plasma parameters is defined numerically.     

光折变有机聚合物中的双色光空间孤子

对光折变有机聚合物中的双色光空间孤子进行了理论分析,证明双色信号光的两个频率成分相互作用可以在折射率改变为正的光折变有机聚合物中形成暗暗和亮暗空间孤子,在折射率改变为负的光折变有机聚合物中形成亮亮和亮暗空间孤子。与单色光孤子的情况不同,对于双色光孤子情况,通过与一形成暗孤子的频率成分相互作用,另一频率成分在折射率改变为正的有机聚合物中也可形成亮孤子;通过与一形成亮孤子的频率成分相互作用,另一频率成分在折射率改变为负的材料中也可形成暗孤子。     

Phase-modulated soliton of self-induced transparency

A theory of optical self-induced transparency for a two-component soliton in the presence of phase modulation is developed. It is shown that, under these conditions, it is possible to generate a vector soliton with characteristic parameters of oscillations with the sum and difference frequencies in the region of the carrier wave frequency. Explicit analytical expressions for nonlinear wave parameters under experimentally implemented conditions are given. In particular case, a well-known solution in the form of a breather is obtained.     

Hirota方程的怪波解及其传输特性研究

求出了高阶Hirota方程在可积条件下的一种精确呼吸子解,并基于此呼吸子解得到了Hirota方程的一种怪波解.在此怪波解的基础上研究了怪波的激发,发现对平面波进行周期性扰动可以激发怪波,对平面波进行高斯扰动可以更快地激发怪波,还可以直接在常数项上增加高斯扰动激发怪波.作为一个实例,采用分步傅里叶方法数值研究了在考虑自频移和拉曼增益时怪波的传输特性,自频移使怪波中心发生偏移,拉曼增益使得怪波分裂得更快,而且拉曼增益值越大怪波分裂得越快,但是拉曼增益对怪波的峰值强度没有明显影响.最后数值模拟了相邻怪波之间的相互作用特点,随着怪波之间距离的减小,怪波将合二为一,成为一束怪波,之后再分裂,并分析了拉曼增益和自频移对怪波相互作用的影响.     

Asymmetric W-shaped and M-shaped soliton pulse generated from a weak modulation in an exponential dispersion decreasing fiber

We study localized waves on continuous wave background in an exponential dispersion decreasing fiber with two orthogonal polarization states. We demonstrate that asymmetric W-shaped and M-shaped soliton pulse can be generated from a weak modulation on continuous wave background. The numerical simulation results indicate that the generated asymmetric soliton pulses are robust against small noise or perturbation. In particular, the asymmetric degree of the asymmetric soliton pulse can be effectively controlled by changing the relative frequency of the two components. This character can be used to generate other nonlinear localized waves, such as dark–antidark and antidark–dark soliton pulse pair, symmetric W-shaped and M-shaped soliton pulse. Furthermore, we find that the asymmetric soliton pulse possesses an asymmetric discontinuous spectrum.     

Dark soliton in one-dimensional Bose–Einstein condensate under a periodic perturbation of trap

The perturbation of a confining trap leads to the collective oscillation of a Bose--Einstein condensate, thereby the propagation of a dark soliton in the condensate is affected. In this study, periodic perturbation is employed to match the soliton oscillation. We find that the soliton dynamics depends sensitively on the coupling between the moving direction of the trap and that of the soliton. The soliton energy/depth evolves periodically, and a relevant shift in the soliton trajectory occurs as compared with the unperturbed case. Overall, the soliton oscillation frequency changes little even if the perturbation amplitude and frequency vary.     

有限宽度背景中的啁啾灰孤子

基于在正常色散区的变系数非线性薛定谔方程,考虑一个带有微扰的参数渐减光纤系统,并利用数值模拟方法,对超高斯型有限宽度背景波和有限宽度背景中啁啾灰孤子的传输进行详细地研究.结果表明,超高斯背景波可以在带有微扰的参数渐减光纤系统中不受负载啁啾灰孤子的影响而稳定传输.当取背景波脉宽与啁啾孤子的初始脉宽比例大于或等于50时,有限宽度背景中啁啾灰孤子的数值结果基本与精确解相吻合.即使选取的背景波脉宽不宽,有限宽度背景中的啁啾灰脉冲仍可以很好的保持其孤子性质.     

Higher-order inertial Alfvén wave dressed solitons,quasiperiodic structures,and chaos in plasmas

The higher-order, low-amplitude inertial Alfvén wave (IAW) dressed soliton and chaos are investigated in a magnetized plasma. In the linear limit, the dispersion relation for propagation of IAWs in plasmas is also obtained in the presence of electron thermal effects and illustrated numerically. It is found that the electron inertial length plays an important role for wave dispersion effects and its phase speed is increased on including the electron temperature in the model. The reductive perturbation method is employed to obtain the first-order IAW Korteweg–de Vries (KdV) soliton and second-order dressed soliton solutions analytically, which gives electron density dip (or rarefactive) structure and moves with super Alfvénic speed in plasmas. The numerical illustrations of the KdV and dressed IAW solitons are also presented by using the laboratory and space plasma parameters given in the literature. Furthermore, a numerical study of quasi-periodicity and chaotic behaviour of IAWs in the presence of external periodic force is also discussed in detail. The effects of plasma beta (which depends on plasma density, electron temperature, and magnetic field intensity) and obliqueness of the wave propagation on the formation of nonlinear Alfvénic wave structures have also been presented.     

Kadomstev-Petviashvili (KP) equation in warm dusty plasma with variable dust charge,two-temperature ion and nonthermal electron

In this work, the propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ion and nonthermal electron is studied. By using the reductive perturbation theory, the Kadomstev-Petviashvili (KP) equation is derived. The energy of the soliton and the linear dispersion relation are obtained. The effects of variable dust charge on the energy of soliton and the angular frequency of linear wave are also discussed.     

Vector soliton of self-induced transparency of a generalized love wave

A theory of acoustic self-induced transparency of a two-component vector soliton for a generalized Love wave is constructed. The three-layer system contains a resonance transition layer with paramagnetic impurity atoms or quantum dots. It is shown that, under these conditions, a vector soliton of the generalized Love wave can be formed. It oscillates at the sum and difference frequencies in the vicinity of the carrier wave frequency. Explicit analytical expressions for the parameters of a nonlinear surface acoustic wave are presented. The parameters depend on the elastic properties of the contacting media, the resonance transition layer, and the transverse structure of the wave. Numerical calculations are carried out for the three-layer Al₂O₃/ZnO/SiO₂ system. The significant difference between the two-component vector soliton and singlecomponent soliton is shown.     

Perturbation of chiral solitons

This paper studies the perturbation of soliton due to the chiral nonlinear Schrödinger's equation by the aid of soliton perturbation theory. The perturbation term that is studied is the quantum potential perturbation of the chiral soliton that is known as Bohm potential. The stable fixed point of the chiral soliton parameters is obtained.     

Weakly dissipative dust acoustic solitons in the presence of superthermal particles

An investigation of the linear and non‐linear properties of low‐frequency electrostatic (dust acoustic) waves in a collisional dusty plasma with negative dust grains, Maxwellian electrons, and κ ‐distributed ions is carried out. Low dust–neutral collisions accounting for dissipation (wave damping effect) is considered. The linear properties of dust acoustic excitations are discussed for varying values of relevant plasma parameters. It is shown that large wavelengths (beyond a critical value) are overdamped. In the limit of low dust–neutral collision rate, we have derived a damped Korteweg de Vries (KdV) equation by using the reductive perturbation technique. Supplemented by vanishing boundary conditions, the time‐varying solution of damped KdV equation leads to a weakly dissipative negative potential soliton. The soliton evolution with the damping parameter and other physical plasma parameters (superthermality, dust concentration, ion temperature) is delineated.     

Solitons of the KP equation in dusty plasma with variable dust charge and two temperature ions: energy and stability

The propagation of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions is analyzed. By using the reductive perturbation theory, the Kadomtsev-Petviashivili (KP) equation is derived. A Sagdeev potential has been investigated. This potential is used to study the stability conditions for existence of solitonic solutions. Also, it is shown that a rarefactive soliton can exist in most of the cases. The energy of the soliton has been calculated and by using the standard normal-mode analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the amplitude, width and energy of soliton and its effects on the angular frequency of linear wave are also discussed.     

Josephson结中混沌孤振子的超辐射

考虑两个耦合的长Josephson结，运用直接微扰法，讨论周期微扰下混沌孤振子的超辐射功率，结果表明：周期微扰下的孤子作混沌运动，当孤子逐渐与周期微扰同步时，辐射功率不断增大，其上限虽受限的有界条件制约，但通常比孤子对的辐射功率更大，理论分析和数值模拟均很好地说明了这一点，这为混沌孤振子的实际应用提供理论依据。     

Optical soliton perturbation in non-Kerr law media: Traveling wave solution

This paper analyses the dynamics of soliton propagation through optical fibers with non-Kerr law nonlinearities. The governing nonlinear Schrödinger equation is integrated in the presence of perturbation terms. The traveling wave hypothesis is used to carry out the integration. Domain restrictions on the soliton parameters are identified in the process. The five forms of nonlinearity that are studied are Kerr-law, power-law, parabolic-law, dual-power law and the log-law nonlinearity. Numerical simulations are presented for each of these nonlinear media.     

Compton散射下多信道平面光波导的空间光孤子开关

应用量子微扰理论和多光子非线性Compton散射模型,对Compton散射下多信道平面光波导的空间光孤子开关进行了研究.结果表明:在横向具有正弦形周期折射率调制的非线性平面光波导的多信道系统中,原先束缚在一个信道中的孤子可以靠由入射和散射光形成的耦合控制光点,通过交叉相位调制横向吸引孤子波束,使孤子从原信道切换到邻近信道,从而实现光孤子开关的功能.控制光点可由耦合光在势谷之间的横向聚焦来实现.散射既能使控制光点的有效强度的阈值和孤子的辐射损耗增大,势垒增高,幅度下降较小,有利于孤子开关的形成;又能使波束展宽较宽,并存在开关被破坏的危险.由此可见,Compton散射下恰当控制入射激光强度是实现孤子开关的关键.     

The window Josephson junction: a coupled linear nonlinear system

We investigate the interface coupling between the two-dimensional sine-Gordon equation and the two-dimensional wave equation in the context of a Josephson window junction using a finite volume numerical method and soliton perturbation theory. The geometry of the domain as well as the electrical coupling parameters are considered. When the linear region is located at each end of the nonlinear domain, we derive an effective one-dimensional model, and using soliton perturbation theory, compute the fixed points that can trap either a kink or antikink at an interface between two sine-Gordon media. This approximate analysis is validated by comparing with the solution of the partial differential equation and describes kink motion in the one-dimensional window junction. Using this, we analyze steady-state kink motion and derive values for the average speed in the one- and two-dimensional systems. Finally, we show how geometry and the coupling parameters can destabilize kink motion.     

Moving near-gap solitons in the nonlinear optical medium

For a one-dimensional nonlinear optical medium with a periodic refraction index, new two-parameter soliton solutions of electrodynamics equations have been found. These solutions represent two interacting waves that propagate in two opposite directions. The oscillation frequency of each wave may fall either into the forbidden gap in the linear spectrum or outside it, and the group velocity may vary from zero to a maximal value that is determined by the parameters of the medium. Algebraic soliton solutions have been found as the limit of the nonlinear solutions, when the nonlinear wave frequency tends to the frequency of one of the linear-spectrum branches.     

Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.     

广义KdV孤子解和广义KdV-Burgers行波解的条件稳定性

对于一类KdV方程的孤子解和一类KdV-Burgers方程的行波解，利用直接扰动法证明了它们具有条件稳定性，即解的稳定性敏感的依赖于方程的参数和初始条件，从而推广和修正了近期文献中关于这些解不稳定的结论. 关键词：