AC-driven damped Toda lattice

The dynamic properties of the ac-driven damped Toda lattice are studied using numerical simulations. The threshold effect of the drive parameter and the stability conditions are investigated by varying the all essential parameters. The collisions of solitons under the influence of the external drive are explored. The drive scheme is also adapted to the continuum system.     

A finite difference method for korteweg-de vries like equation with nonlinear dispersion

The Korteweg-de Vries (KdV) equation has been generalized by Rosenau and Hyman [3] to a class of partial differential equations (PDEs) which has solitary wave solution with compact support. These solitary wave solutions are called compactons. Compactons are solitary waves with the remarkable soliton property, that after colliding with other compactons, they reemerge with the same coherent shape. These particle like waves exhibit elastic collision that are similar to the soliton interaction associated with completely integrable systems. The point where two compactons collide are marked by a creation of low amplitude compacton-anticompacton pair. These equations have only a finite number of local consevation laws. In this paper, an implicit numerical method has been developed to solve the K(2,3) equation. Accuracy and stability of the method have been studied. The analytical solution and the conserved quantities are used to assess the accuracy of the suggested method. The numerical results have shown that this compacton exhibits true soliton behavior.

     

正常色散光纤消啁啾的孤子传输实验

利用正常色散光纤消啁啾成功地进行了１Ｇｂｉｔ／ｓ，２３公里的光弧子传输，观察到了一阶和高阶孤子传输现象，通过实验发现：采用适当长度的正常色散光纤消负啁啾，不仅能够压窄负啁啾的脉宽而且能够压窄频谱。     

Effect of Soliton Propagation in Fiber Amplifiers

The propagation of optical solitons in fiber amplifiers is discussed by considering a model that includes linear high order dispersion, two-photon absorption, nonlinear high-order dispersion, self-induced Ramam and five-order nonlinear effects.Based on traveling wave method, the solutions of the nonlinear Schrodinger equations, and the influence on soliton propagation as well as high-order effect in the fiber amplifier are discussed in detail.It is found that because of existing five-order nonlinear effect ,the solution is not of secant hyperbola type, but shows high gain state of the fiber amplifier which is very favourable to the propagation of solitons.     

Galerkin finite element solution for Benjamin–Bona–Mahony–Burgers equation with cubic B-splines

In this article, we study solitary-wave solutions of the nonlinear Benjamin–Bona–Mahony–Burgers(BBM–Burgers) equation based on a lumped Galerkin technique using cubic B- spline finite elements for the spatial approximation. The existence and uniqueness of solutions of the Galerkin version of the solutions have been established. An accuracy analysis of the Galerkin finite element scheme for the spatial approximation has been well studied. The proposed scheme is carried out for four test problems including dispersion of single solitary wave, interaction of two, three solitary waves and development of an undular bore. Then we propose a full discrete scheme for the resulting IVP. Von Neumann theory is used to establish stability analysis of the full discrete numerical algorithm. To display applicability and durableness of the new scheme, error norms $L_2$, $L_{\infty }$ and three invariants $I_1,I_2$ and $I_3$ are computed and the acquired results are demonstrated both numerically and graphically. The obtained results specify that our new scheme ensures an apparent and an operative mathematical instrument for solving nonlinear evolution equation.     

新型LT码编译码方法及其在认知无线电中的应用

Luby变换(LT)码作为一种抗干扰编码技术,应用于认知无线电系统,可提高次用户数据传输的可靠性。编译码是影响LT码抗干扰性能的关键因素。为提高数据传输的可靠性和速度,该文提出一种适用于认知无线电系统的LT码联合泊松鲁棒孤子分布-叠层(CPRSD-H)编译码算法。编码过程中,编码器首先采用CPRSD进行编码产生编码分组和编码矩阵,随后通过编码矩阵中度数为1和度数为2对应的列向量携带双层信息：度数为1和度数为2的编码分组和与其相连接的输入分组的连接关系;部分原始数据信息。译码过程中,译码器首先通过第1层存储信息采用置信传播(BP)算法译码完成,随后一些未被成功译出的信息再通过第2层存储信息进行填补。仿真结果表明,将CPRSD-H编译码算法应用于认知无线电系统中,能够显著降低LT码的误比特率(BER),提高次用户有效吞吐量以及加快LT码编译码速度。

     

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.     

光孤子通信系统（上）

本讲座介绍光孤子通信系统的概貌［１］，着重叙述光孤子的物理概念及其特性、光纤损耗对光孤子的影响以及对光孤子放大怎样补偿光纤损耗，从而使光孤子传输数千公里后仍保持波形和幅度不变。     

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.