双包层椭圆光波导解析解

解析求解了双包层椭圆光纤中的波动方程，得到了模式精确解有模式特征方程。对基模的特征方程进行了数值计算，给出了不同椭圆比下的归一化双折射和模间色散随归一化频率的变化关系曲线，并与高斯近似解的结果进行了比较。     

Improved Speed and Shape of Ion-Acoustic Waves in a Warm Plasma

The basic set of fluid equations can be reduced to the nonlinear Kortewege-de Vries (KdV) and nonlinear Schrödinger (NLS) equations. The rational solutions for the two equations has been obtained. The exact amplitude of the nonlinear ion-acoustic solitary wave can be obtained directly without resorting to any successive approximation techniques by a direct analysis of the given field equations. The Sagdeev's potential is obtained in terms of ion acoustic velocity by simply solving an algebraic equation. The soliton and double layer solutions are obtained as a small amplitude approximation. A comparison between the exact soliton solution and that obtained from the reductive perturbation theory are also discussed.     

Nearly linear dynamics of nonlinear dispersive waves

Dispersive averaging effects are used to show that the Korteweg-de Vries (KdV) equation with periodic boundary conditions possesses high frequency solutions, which behave nearly linearly. Numerical simulations are presented, which indicate the high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.     

A uniform approximation to the scattering and propagation problem for a stratified Bi-anisotropic slab

The scattering and propagation problem for time-harmonic waves in a stratified bi-anisotropic slab is considered. Based upon the identification of the left- and right-moving modes, and on a boundedness assumption concerning the space and frequency dependence of the physical parameters, a sequence of approximate solutions which converge absolutely and uniformly to the exact solution are derived. In particular, if the magnetoelectric coupling is small and the permittivity and permeability vary slowly, the approximate solutions converge so fast that the first approximation already gives a satisfactory approximation. With the present approximation method, approximate solutions valid for all frequencies can be obtained in explicit form.     

Mode-field half widths of Gaussian approximation for fundamental mode of two kinds of optical waveguides

This paper analyzes the characteristic of matching effciency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Gaussian approximation for the fundamental mode should be defined according to the maximal matching effciency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching effciency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.     

Decaying periodic-wavetrain and solitary-vortex exact solutions for two-dimensional planetary viscous flows

Summary We give Taylor-Kovasznay solutions for two-dimensional motions in a layer of viscous fluid on a rotating globe in the β-plane approximation. These solutions represent travelling-wave-type periodic wavetrains and solitary vortices which decay away in time due to viscous effects. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Difference-Frequency Generation Among Ultrashort Optical Pulses in Quasi-Phase-Matching Waveguides

A theoretical model of ultrashort pulse difference-frequency generation (DFG) is presented and developed with quasi-phase matching (QPM) gratings in the undepleted-pump, unamplified-signal approximation. An analytic solution to a case of ultrashort pulse pumped DFG process, including group-velocity mismatching effects and input pulses with frequency chirp and time delay, is obtained. The influences of group-velocity mismatching effects and input signal pulse parameters on the conversion efficiency and output converted pulse characteristics are analyzed and discussed. The results indicate that the conversion efficiency is increased due to the enhancement of pump and signal interaction. The output pulse is inevitable compressed under pulsed pumping and can be compensated by introducing the initial frequency chirp and time delay.     

Solution procedure of residue harmonic balance method and its applications

This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems. In this solution procedure, no small parameter is assumed. The harmonic residue of balance equation is separated in two parts at each step. The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement. The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again. Three kinds of different differential equations involving general, fractional and delay ordinary differential systems are given as numerical examples respectively. Highly accurate limited cycle frequency and amplitude are captured. The results match well with the exact solutions or numerical solutions for a wide range of control parameters. Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems. Moreover, the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.     

Thermodynamic parameterization

A new method of succesive construction of a solution is developed for problems of strongly nonequilibrium Boltzmann kinetics beyond normal solutions. Firstly, the method provides dynamic equations for any manifold of distributions where one looks for an approximate solution. Secondly, it gives a successive procedure of obtaining corrections to these approximations. The method requires meither small parameters, nor strong restrictions upon the initial approximation; it involves solutions of linear problems. It is concordant with the H-theorem at every step. In particular, for the Tamm-Mott-Smith approximation, dynamic equations are obtained, an expansion for the strong shock is introduced, and a linear equation for the first correction is found.     

Electron acceleration by tightly focused radially polarized few-cycle laser pulses

Within the framework of plane-wave angular spectrum analysis of the electromagnetic field structure, a solution valid for tightly focused radially polarized few-cycle laser pulses propagating in vacuum is presented. The resulting field distribution is significantly different from that based on the paraxial approximation for pulses with either small or large beam diameters. We compare the electron accelerations obtained with the two solutions and find that the energy gain obtained with our new solution is usually much larger than that with the paraxial approximation solution.     

非旋转性前进波Euler与Lagrange解间的转换

对等深水中非旋转性的前进重力波动场,以求得的Euler与Lagrange两种形式至第三阶的解,按照同一流体质点在相同时间与位置处其流速唯一与质量守恒性及在自由表面水位处Euler形式解与Lagrange形式解为同一值的特性,来推导二者可相互转换.由连续的Taylor级数展开,考虑波动场中各流体质点的运动轨迹与运动周期,将已知的Euler形式解转换成完全未知的Lagrange形式解,解决了以往成果中出现含时间的不合理的共振项,以及无法得到与Euler系统不同的Lagrange形式的流体质点运动频率与平均运动 关键词： 非旋转性前进波 Euler-Lagrange转换 质点运动轨迹 质点运动频率     

The residue harmonic balance for fractional order van der Pol like oscillators

When seeking a solution in series form, the number of terms needed to satisfy some preset requirements is unknown in the beginning. An iterative formulation is proposed so that when an approximation is available, the number of effective terms can be doubled in one iteration by solving a set of linear equations. This is a new extension of the Newton iteration in solving nonlinear algebraic equations to solving nonlinear differential equations by series. When Fourier series is employed, the method is called the residue harmonic balance. In this paper, the fractional order van der Pol oscillator with fractional restoring and damping forces is considered. The residue harmonic balance method is used for generating the higher-order approximations to the angular frequency and the period solutions of above mentioned fractional oscillator. The highly accurate solutions to angular frequency and limit cycle of the fractional order van der Pol equations are obtained analytically. The results that are obtained reveal that the proposed method is very effective for obtaining asymptotic solutions of autonomous nonlinear oscillation systems containing fractional derivatives. The influence of the fractional order on the geometry of the limit cycle is investigated for the first time.     

Dynamics of breathers and rogue waves in scalar and multicomponent nonlinear systems

In this paper, we propose a new method, the variable separation technique, for obtaining a breather and rogue wave solution to the nonlinear evolution equation. Integrable systems of the derivative nonlinear Schrödinger type are used as three examples to illustrate the effectiveness of the presented method. We then obtain a family of rational solutions. This family of solutions includes the Akhmediev breather, the Kuznetsov-Ma breather, versatile rogue waves, and various interactions of localized waves. Moreover, the main characteristics of these solutions are discussed and some graphics are presented. More importantly, our results show that more abundant and novel localized waves may exist in the multicomponent coupled equations than in the uncoupled ones.     

载流有界等离子体柱中的剪切阿尔芬波涡旋

本文采用二流体方程组，研究低β（ｍｅ／ｍｉ＜＜β＜＜１）载流有界等离子体柱中的非线性剪切阿尔芬波，求得一类新的电磁涡旋解。在这类解中，扰动电场和扰动磁场的局域结构由单极部分和多极部分组成，而扰动密度是多极涡旋结构。这些相干结构以一定的角速度整体地绕等离子体柱轴运行。对于本文所取的参数，平衡电流对扰动电磁场和密度的涡旋结构无影响。     

Rogue waves: New forms enabled by GPU computing

A method to determine parameters governing periodic Riemann theta function rogue-wave solutions to the nonlinear Schrödinger equation is presented. A map of parameter values leading to candidate solutions is developed. In addition to candidate solutions, an overview of qualitative aspects of the solution space can be gained from this map. Based on these findings, several new extreme wave solutions are presented. Although the computations required to determine the map are quite demanding, it is shown that these computations can be efficiently accelerated with a parallel computing architecture. A general purpose computing on a graphics processor unit (GPGPU) implementation yielded a 400× acceleration over a single threaded high level implementation. This acceleration enabled exploration and examination of the solution space, which otherwise would not have been possible. In addition, the solution methodology presented here can be extended to explore other classes of solutions.     

A Method for Solving Initial-value Problem and Finding Exact Solutions of Nonlinear Partial Differential Equations

Homogeneous balance method for solving nonlinear partial differential equation(s) is extended to solving initial-value problem and getting new solution(s) from a known solution of the equation(s) under consideration. The approximate equations for long water waves are chosen to illustrate the method, infinitely many simple-solitary-wave solutions and infinitely many rational function solutions, especially the closed form of the solution for initial-value problem, are obtained by using the extended homogeneous balance method given here.     

Electromagnetic fields in a waveguide with a modulated filling near the frequency of resonant interaction between the signal wave and modulation wave

The interaction between a transverse-electric (TE) signal wave and a periodically modulated wave in a waveguide of arbitrary cross-section is considered. The wave equation for the potential of TE field near the frequency of resonant interaction between the signal wave and modulation wave is solved, using the double-scale expansion method. The fields in the first approximation with respect to the modulation indices are obtained.