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.     

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.     

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.     

Influence of iron doping on spatial soliton formation and fixing in lithium niobate crystals

We analyse the feasibility of using iron-doping in lithium niobate in order to stabilize and permanently fix light-induced integrated structures. General 3D optical interconnections were realized in bulk lithium niobate crystals by means of soliton waveguides exploiting the enhanced photorefractive properties obtainable using specific iron doping. We report an enhancement of the photorefractive properties in doped crystals that can be considered for permanently fixing the integrated circuits. This work opens new directions for realizing permanent self-assembled and self-aligned integrated electro-optic devices and photonic circuits.     

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.     

非相对论量子流体中的孤立子运动特征

对在非相对论情况下描述量子流体运动的 GP 方程进行了全面地分析,得出了量子流体的运动是一种特殊的孤立子运动的结论.进而利用这个解及其特性解释了,在超流体中所观察到的宏观量子效应.     

光纤通信技术的发展与探索

本文概述了光纤通信的发展动态,讨论了非线性光纤通信新技术和孤子技术,提出了全光光纤通信的概念。     

Mechanism of multiple pulse formation in the normal dispersion regime of passively mode-locked fiber ring lasers

We identify the spectral gain filtering as a mechanism of multiple pulse formation in a fiber laser passively mode-locked through nonlinear polarization rotation operating in the normal dispersion regime. A correlation is theoretically established between the spectral gain bandwidth and the possibility for the laser to deliver several pulses by cavity round-trip: narrow spectrum favours multiple pulsing. Moreover the model allows to show that spectral loss or gain filtering are equivalent with respect to their consequences on the multiple pulsing regime. Experimental results obtained with an erbium-doped fiber laser and an ytterbium-doped fiber laser confirm the theoretical calculations. In addition, an indirect confirmation of the influence of the spectral filtering is proposed using an experimental setup involving a unique laser.     

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