单模光纤中超快受激拉曼散射的反斯托克斯波

由光纤中光的基本传输方程出发 ,利用慢变振幅近似 ,给出了包含反斯托克斯波的光纤超快受激拉曼散射的耦合波方程。以此为基础讨论连续、超快受激拉曼散射中泵浦波、斯托克斯和反斯托克斯波的耦合 ,分析了单模光纤相位匹配和群速匹配对光纤超快受激拉曼散射反斯托克斯波产生的影响     

Varieties of solitons and solitary waves

A summary is presented of the principal types of completely integrable partial differential equations having soliton solutions. Each type is derived from an appropriate physical model of an electromagnetic wave problem, with the intention to show how known mathematical results apply to a coherent class of physical problems in electromagnetic waves. The non-linear Schrödinger (NS) equation appears when the induced non-linear dielectric polarization is expanded in a series of powers of the electric field, only the linear and third-order polarizations are retained, and the temporal spectrum of the wave is a narrow band far removed from any resonance of the medium. The sine-Gordon equation appears from a similar optical model of propagation in a dielectric consisting of identical 2-level atomic systems, but resonance occurs between the carrier frequency of the wave and the transition frequency of the atoms. The Boussinesq and Korteweg– de Vries equations appear at different levels of approximation to a potential wave on a transmission line having a non-linear capacitance such that the charge stored is a non-linear function of the line potential. In all cases the evolution variable is the propagation distance; the transverse variable is time, but in the case of the NS equation it may alternatively be a spatial coordinate, giving rise to the possibility of spatial solitons as well as temporal solitons for NS-type problems. Two examples are derived of non-integrable Hamiltonian systems having spatial solitary waves, namely the second-order cascade interaction and vector spatial solitary waves of the third-order interaction, and a brief survey of the analytical solutions for the plane waves and solitary waves of these two types is presented. Finally, the addition of a second spatial dimension to the non-linear transmission line problem leads to the Kadomtsev–Petviashvili equations, and a further approximation for weakly modulated travelling waves leads to the Davey–Stewartson equations. Both of these completely integrable systems support combined spatial–temporal solitons.     

Nonlinear propagation of weakly relativistic ion-acoustic waves in electron–positron–ion plasma

This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, the Korteweg–de Vries (KdV) equation is derived using the well-known reductive perturbation method. The integration of the derived equation is carried out using the ansatz method and the generalized Riccati equation mapping method. The influence of plasma parameters on the amplitude and width of the soliton and the electrostatic nonlinear propagation of weakly relativistic ion-acoustic solitary waves are described. The obtained results of the nonlinear low-frequency waves in such plasmas may be helpful to understand various phenomena in astrophysical compact object and space physics.     

Solitary wave solutions for the regularized long-wave equation

The regularized long-wave equation has been solved numerically using the collocation method based on the Adams-Moulton method for the time integration and quintic B-spline functions for the space integration. The method is tested on the problems of propagation of a solitary wave and interaction of two solitary waves. The three conserved quantities of motion are calculated to determine the conservation properties of the proposed algorithm. The L _?? error norm is used to measure the difference between exact and numerical solutions. A comparison with the previously published numerical methods is performed.     

Combined optical solitary waves of the Fokas—Lenells equation

In this work, we investigate the Fokas–Lenells equation describing the propagation of ultrashort pulses in optical fibers when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrö dinger equation are retained. In addition to group velocity dispersion and Kerr nonlinearity, the model involves both spatio-temporal dispersion and self-steepening terms. A class of exact combined solitary wave solutions of this equation is constructed for the first time, by adopting the complex envelope function ansatz. The influences of spatio-temporal dispersion on the characteristics of combined solitary waves is also discussed.     

The role of Cairns–Gurevich distributed electrons on obliquely propagating ion-acoustic waves

We used a new distribution of electrons in a two-component magnetized plasma to study the non-linear ion-acoustic solitary structures. The distribution called “Cairns–Gurevich distribution” describes simultaneously the evolution of the energetic electrons and those trapped in the plasma potential well. A modified KdV equation describing the non-linear comportment of the ion-acoustic wave (IAW) was found by using the standard reductive perturbation technique and the appropriate independent variables. The behaviour of the soliton by changing the plasma parameters has been investigated, and we demonstrated that by decreasing the non-thermality parameter, the soliton solution amplitude is enhanced. In addition, we have discussed the growth rate of the solitary waves by calculating the instability criterion. Through discussion, we have conferred how different plasma parameters, such as the trapping, non-thermality, Mach number, obliqueness via the angle of propagation, and magnetic field via the ion-cyclotron frequency, can affect the solitary wave structures. This kind of theoretical studies can be relevant to understand the non-linear propagation of IA solitary waves plasmas of electrons and particles in laser-plasma interaction, pulsar magnetosphere, the auroral zone, and the upper ionosphere, where plasma with trapped and energetic electrons are often present.     

On the generalized Kadomtsev-Petviashvili equation with generalized evolution and variable coefficients

In this Letter, the existence of the solitary wave solution of the Kadomtsev-Petviashvili equation with generalized evolution and time-dependent coefficients will be studied. We use the solitary wave ansätze-method to derive these solutions. A couple of conserved quantities are also computed. Moreover, some figures are plotted to see the effects of the coefficient functions on the propagation and asymptotic characteristics of the solitary waves.     

Optical Solitary Waves in Fourth-Order Dispersive Nonlinear Schr(o)dinger Equation with Self-steepening and Self-frequency Shift

By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitarywave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.     

修正高阶非线性薛定锷方程的解析孤波解

解析求解了考虑喇曼自频移效应后的修正高阶非线性薛定锷方程.为了获得精确解,引入了非线性增益和失谐效应.结果给出精确亮孤波解和暗孤波解的表达式,同时给出了两种解存在的参量条件,并且指出亮孤波解存在于负三阶色散区,而暗孤波解存在于正三阶色散区.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

Nonparaxial one-dimensional spatial solitons

Scalar and vector nonlinear nonparaxial evolution equations are developed for propagation in two-dimensions. Using standard soliton scalings, it is found that nonparaxial propagation is accompanied by higher-order linear and nonlinear terms and an effective quintic nonlinear index. The presence of an intrinsic quintic nonlinearity arising from chi((5)) must also be considered at the order of the analysis. These terms represent corrections to the well-known nonlinear Schrodinger equation. Exact and approximate solutions to these higher-order evolution equations are obtained and are shown to exhibit quasi-soliton behavior based on propagation and collision studies. (c) 2000 American Institute of Physics.     

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.     

Exact solutions in nonlinearly coupled cubic–quintic complex Ginzburg–Landau equations

Exact analytical solutions for pulse propagation in a nonlinear coupled cubic–quintic complex Ginzburg–Landau equations are obtained. Three families of solitary waves which describe the evolutions of progressive bright–bright, front–front, dark–dark and other families of solitary waves are investigated. These exact solutions are analyzed both for competition of loss or gain due to nonlinearity and linearity of the system. The stability of the solitary waves is examined using analytical and numerical methods. The results reveal that the solitary waves obtained here can propagate in a stable way under slight perturbation of white noise and the disturbance of parameters of the system.     

Solitary wave emission from a non-linear waveguide with a PTS cladding

We present numerical simulations of solitary wave emission from a waveguide in which the cladding is the non-linear material polydiacetylene para-toluene sulfphonate (PTS). In addition to a self-focusing cubic non-linearity PTS exhibits a defocusing quintic non- linearity, which imposes a limit on the peak non-linear index change. The influence of this limiting on solitary wave emission is studied in detail in one transverse dimension, and we show that it can increase the fraction of the incident power transferred into the emitted solitary wave. Fabrication issues arising from the limiting are also discussed. Numerical simulations in two transverse dimensions are also presented showing stable emitted solitary waves due to the stabilizing effect of the limiting, in contrast to the self-focusing collapse which occurs for a cubic non-linearity.     

Ion-acoustic waves at the night side of Titan's ionosphere: higher-order approximation

Nonlinear solitary waves are investigated for a plasma system at the night side of Titan's ionosphere. The plasma model consists of three positive ions, namely C_2H_5~+, HCNH~+, and C_3H_5~+, as well as Maxwellian electrons. The basic set of fluid equations is reduced to a Korteweg de-Vries(KdV) equation and linear inhomogeneous higher order KdV(LIHO-KdV) equation.The solitary wave solutions of both equations are obtained using a renormalization method. The solitary waves' existence region and the wave profile are investigated, and their dependences on the plasma parameters at the night side of Titan's ionosphere are examined. The solitary waves' phase velocities are subsonic or supersonic, and the propagating pulses are usually positive. The effect of higher-order corrections on the perturbation theory is investigated. It is found that the higher-order contribution makes the amplitude slightly taller, which is suitable for describing the solitary waves when the amplitude augments.     

Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients

Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with time-dependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic, double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.     

Domain wall motion in ferromagnets modelled by a quintic complex Ginzburg-Landau equation

A quintic complex Ginzburg-Landau equation is derived from a Landau-Lifshitz-Gilbert equation and is used to describe the magnetization dynamics in a one-dimensional uni-axial ferromagnet. Trough the use of suitable approximations, we derive the magnetic solitary wave excitations solutions which have pulse-like shapes. Subsequent numerical simulations reveal domain wall propagation.     

耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。     

On some exact solutions of slightly variant forms of Yang’s equations and their graphical representations

The equations obtained by Yang while discussing the condition of self-duality of SU(2) gauge fields on Euclidean four-dimensional space have been generalized. Exact solutions and their graphical representations for the generalized equation (for some particular values of the parameters) have been reported. They represent interesting physical characteristics like waves with spreading solitary profile, spreading wave packets, waves with pulsating solitary profile (between zero and a maximum), waves with oscillatory solitary profile and chaos.      

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

The purpose of this paper is to report the feasibility of constructing high-order rogue waves with controllable fission and asymmetry for high-dimensional nonlinear evolution equations.Such a nonlinear model considered in this paper as the concrete example is the(3+1)-dimensional generalized Boussinesq(gB) equation,and the corresponding method is Zhaqilao’s symbolic computation approach containing two embedded parameters.It is indicated by the(3+1)-dimensional gB equation that the embedded param...