Efficient numerical algorithms for the solution of “good” Boussinesq equation in water wave propagation

This paper proposes three fast and high accuracy numerical methods for solving a nonlinear partial differential equation (PDE) describing water waves and called the Boussinesq (Bq) equation. We numerically solve the Bq equation with fourth-order time-stepping schemes in combination with discrete Fourier transform. We discretize the original PDE with discrete Fourier transform in space and obtain a system of ordinary differential equations (ODEs) which will be solved with fourth-order time-stepping methods. After transforming the equation to a system of ODEs, the linear operator is not diagonal, but we can implement the methods such as diagonal case which reduces the CPU time. Comparing numerical solutions with analytical solutions demonstrates that those methods are accurate and readily implemented. Also we investigate the conservation of mass for Bq equation.     

Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein-Gordon equation

This paper aims to obtain approximate solutions of the Nonlinear Klein-Gordon (NLKG) equation by employing the Boundary Integral Equation (BIE) method and the Dual Reciprocity Boundary Element Method (DRBEM). This method is improved by using a predictor-corrector scheme to the nonlinearity which appears in the problem. We employ the time stepping scheme to approximate the time derivative, and the Linear Radial Basis Functions (LRBFs), are used in the Dual Reciprocity (DR) technique. To confirm the accuracy of the new approach, the numerical results of a Double-Soliton and a problem with inhomogeneous terms are compared with analytical solutions and for the examples possessing single and periodic waves, two conserved quantities associated to the (NLKG) equation, the energy and the momentum are investigated.     

A modified explicit numerical scheme for the two-dimensional sine-Gordon equation

Abstract

A fourth-order rational approximant to the matrix-exponential term in a three-time-level recurrence relation is used to transform the two-dimensional sine-Gordon equation into a second-order initial-value problem. The resulting nonlinear system is solved using an appropriate predictor–corrector (P-C) scheme in which the predictor is an explicit one of second order. The procedure of the corrector is accelerated by using a modification (MPC) in which the already evaluated values are used for the corrector. Both the nonlinear method and the predictor–corrector are analysed for local truncation error and stability. The MPC scheme has been tested on line and circular ring solitons known from the literature, and numerical experiments have proved that there is an improvement in accuracy over the standard predictor–corrector implementation.     

Existence,stability, and scattering of bright vortices in the cubic–quintic nonlinear Schrödinger equation

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variational approach is used to predict the radial shape of the vortex soliton, using the radial equation, yielding results very close to those obtained from numerical solutions. Previously known existence bounds for the solitary vortices are recovered by means of this approach. The 1D azimuthal equation of motion is used to analyze the modulational instability of the vortex solitons. The semi-analytical predictions – in particular, the critical intrinsic frequency of the vortex soliton at the instability border – are compared to systematic 2D simulations. We also compare our findings to those reported in earlier works, which featured some discrepancies. We then perform a detailed computational study of collisions between stable vortices with different topological charges. Borders between elastic and destructive collisions are identified.     

光孤子传输基础及其系统关键技术

光孤子具有传输不变形的特性，是光纤通信系统中最理想的信息载体，因此简要阐述了光孤子的成形机制及其传输理论，并介绍了光孤子传输系统构成与其所涉及到的关键技术，最后探讨了光孤子传输系统的研究现状及发展前景。     

Wavelet Beam Propagation Method for Study the Integrated Optical Waveguide

A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide.The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation.Results of numerically simulating the injected field at z=0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides(with linear and/or nonlinear refractive index),which are similar to those in the related publications.Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator.The iterative process needsfewer steps to be stable.Also,when the light wave meets the changes of mediums ,the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.     

光纤孤子通信简述

光纤孤子通信是当前通信技术研究的热门课题之一。根据有关资料,本文对这一技术的发展脉络作了概述。对光纤孤子的形成,传输和系统设计方案作了重点介绍。     

Suppression of Soliton Timing Jitters in Fibers with Random Birefringence by Periodical Polarization Modulation

Periodical polarization modulation scheme is proposed to suppress timing jitters induced by frequency fluctuations between two polarization components of solitons. In periodical polarization modulation scheme, the polarization states of the soliton are modulated to excite equally for suppressing timing jitters induced by two unequal polarization components in the soliton trapping. Moreover, polarization modulation can weaken the effect of random birefringence on the soliton pulses in each relay distance. The numerical result shows that the soliton timing jitters are suppressed by our proposed method.     

聚合物半导体聚乙炔的热激电流谱研究

本文首次给出聚合物半导体材料聚乙炔(CH)_x的热激电流(TSC)谱,观察到聚乙炔的异构化现象,并获得关于聚乙炔极化现象的新结果。本文还给出按照理论公式由实验测得的热激电流峰曲线求得相应激活能的计算机拟合程序     

Two Schemes for a Soliton Transmission with Er^3＋—doped Fiber Amplifier

This paper shall two schemes for soliton transmission with Er^3 -doped fiber amplifier(EDFA).To compared with second scheme,The first scheme will most likely de dominant.