光纤中孤子传输的量子场理论

本文直接对电磁场进行量子化，用密度矩阵描述光纤中的孤子，从量子光学的主方程出发推出Ｐ表示的福克－普朗克方程，从而引出量子包络孤子在光纤中传输的准经典的非互性薛定谔方程，最后介绍了方程的应用。     

Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)

In this paper the meshless local radial point interpolation method (LRPIM) is adopted to simulate the two-dimensional nonlinear sine-Gordon (S-G) equation. The meshless LRPIM is one of the “truly meshless” methods since it does not require any background integration cells. In this case, all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. A technique is proposed to construct shape functions using radial basis functions. These shape functions which are constructed by point interpolation method using the radial basis functions have delta function property. The time derivatives are approximated by the time-stepping method. In order to eliminate the nonlinearity, a simple predictor-corrector scheme is performed. Numerical results are obtained for various cases involving line and ring solitons. Also the conservation of energy in undamped sine-Gordon equation is investigated.     

Commutativity of source generation procedure and Bäcklund transformation: A BKP equation

The source generation procedure is applied to a BKP-type equation and a modified BKP-type (m-BKP) equation, respectively. As a result, a BKP equation with self-consistent sources (ESCS) and a m-BKP ESCS are derived. It is also proved that the bilinear m-BKP ESCS constitutes a bilinear Bäcklund transformation for the BKP ESCS. This means that the commutativity between the source generation procedure and Bäcklund transformation is valid for the BKP equation.     

Soliton perturbation theory for a higher order Hirota equation

Solitary wave evolution for a higher order Hirota equation is examined. For the higher order Hirota equation resonance between the solitary waves and linear radiation causes radiation loss. Soliton perturbation theory is used to determine the details of the evolving wave and its tail. An analytical expression for the solitary wave tail is derived and compared to numerical solutions. An excellent comparison between numerical and theoretical solutions is obtained for both right- and left-moving waves. Also, a two-parameter family of higher order asymptotic embedded solitons is identified.     

Elastic axonemal model: Solitary wave shapes

We introduce an elastic beam Bernoulli–Euler model for the axoneme (cytoskeletal inner core of eukaryotic cells appendages) whose dynamics is controlled by internally generated torques at the inflexion points of the beam. We calculate the geometrical and the mechanical parameters of the axoneme, and compared them with experimental data. We make predictions about nonlinear shapes, including possible solitary waves in the curvature, which can explain certain swimming patterns of the cells.     

Theoretical simulations of proton conductivity: Basic principles for improving the proton conductor

Classical molecular dynamics (MD) simulations of proton conduction have been performed, to get insight into basic principles of potential improvements of proton conductivity in polyelectrolyte membranes. For the simulations the reactive force field for water (RWFF) was used, which allows bond dissociation of water, acids and hydronium ions. The effects are shown to be fundamental relevance for the diffusion of protons in membranes. One and two-dimensional conductors, and a Nafion™ membrane have been modeled in our simulations. The two-dimensional model imitates a metal phosphate; the one-dimensional model imitates an idealized pore of hydrated Nafion membranes. The MD simulations of proton conductivity of the metal phosphate show the dissociation of the acid POH groups and their participation in the proton transport. Several simulations are performed with acids of different strength and the effect of the acid’s strength on the diffusion and on the conductivity is analyzed. The importance of the ion coupling on the conductivity is firstly proved in tubes, which imitate an ideal pore inside a membrane. Afterwards, the coupling is investigated in a real hydrated Nafion membrane by a non-equilibrium MD simulation. The results suggest a soliton-like behavior for proton conductivity in membranes.     

孤子激光器及其在现代科学技术中的应用

孤子激光器在光纤孤子通信、光学计算机、超高速现象的研究、超高速光电子器件的研制等方面有其独特的应用。本文介绍了几种常用孤子激光器的结构、原理以及它在现代科学技术方面的应用。     

各种扰动源产生孤立子波的研究

本文就四种不同形式的扰动在浅水中生成孤立子波的问题进行了研究。这里采用的理论基础是Boussinesq型非线性色散长波模型。非线性偏微分方程组按初-边值问题用有限差分法数值求解,这里包括对开边界条件的近似处理。 数值计算实例给出了四种不同扰动源生成孤立子波的条件和规律。由对计算结果的分析比较,可以发现当外界与流体间有一定方式的质量、动量或能量(动能、位能)交换时,只要满足一定的条件均能生成孤立子波。     

Analytical Studies on 980 nm Pumped Erbium—doped Fiber Amplifiers

Modeled with a three-level-atom appropriate to 980nm pumped ampifiers,analytical solutions have been deduced for the rate equations of erbium-doped fiber amplifiers.Various key parameters of the amplifiers have been specified.     

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashion as finite difference methods. Numerical results are obtained for various cases involving line and ring solitons.