Two-dimensional commensurate soliton structures

A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.     

掺锗硅基高非线性光纤超连续光源研究

利用非线性偏振旋转锁模掺铒光纤激光器和1100m长的掺锗硅基高非线性光纤制作了超连续光源,获得了从1150～1750nm的超宽带输出光谱,其中1150～1350nm波段光谱起伏小于3dB,1600～1700nm波段平坦度优于1dB,并有很好的向长波延展空间。光谱展宽的机理为孤子分裂与受激拉曼散射,而四波混频使光谱进一步展宽。     

Higher-Dimensional KdV Equations and Their Soliton Solutions

A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.     

A Hierarchy of Integrable Lattice Soliton Equations and New Integrable Symplectic Map

Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a Bäcklund transformation for the resulting integrable lattice equations. At last, conservation laws of the hierarchy are presented.     

Darboux Transformation for Tzitzeica Equation

We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem. The explicit solution of Tzitzeica equation is obtained.     

高斯型空间光孤子相互作用的数值研究

 通过数值模拟的方法,对高斯孤子在对数型饱和非线性介质中的相互作用进行了研究,考查了两光束间的相对振幅和相对相位对其相互作用的影响。结果表明：高斯孤子之间的相互作用敏感地依赖于两光束间的相对振幅和相对相位。在不同的振幅差异范围内,光束间的主要作用交替地表现为相互排斥和相互吸引,并由于高斯孤子的不稳定性,导致了光束在碰撞后以一种尺寸周期性变化的呼吸模式传输。随着相对相位的增大,两光束间始终持续地表现出强烈的排斥作用,直到相对相位增加到一个2π周期之后。而且碰撞之后,光束也都以呼吸模式进行传输,其分离的角度越大,呼吸就越明显。     

Gray photorefractive polymeric optical spatial solitons

We show that gray spatial optical solitons are possible in biased photorefractive polymers under steady-state conditions. We find that for a given material parameter the absolute value of a gray photorefractive polymeric soliton's phase decreases with an increase in the beam's grayness, whereas it increases with the material parameter for a given beam's grayness and that the full width half maximum (FWHM) of the gray soliton beam's intensity increases with the beam's grayness when the normalized background intensity and the material parameter are fixed and decreases with an increase in the normalized background intensity when the material parameter is fixed. On the other hand, we also show that N coupled beam evolution equations in biased photorefractive polymers can exhibit multicomponent gray solitons. These multicomponent gray solitons can be obtained provided that the N coupled beams share the same polarization, wavelength, and are incoherent with one another. The characteristics and stability properties of these multicomponent gray solitons are also discussed in detail.     

光诱导准一维光子晶格中离散空间光孤子的相互作用

基于分步束传播法数值分析了离散空间光孤子在准一维光诱 导光子晶格中的相干与非相干相互作用过程. 结果表明: 对于相干孤子, 同相时相互吸引, 反相时相互排斥. 然而, 由于非线性响应的各向异性, 横向排布的非相干孤子会因间隔波导数目的增加而由相互吸引变为相互排斥. 并且, 沿对角方向排布的两个非相干孤子在孤子相 互作用力和布拉格反射的共同影响下, 会呈现出"钟摆式"振荡传输现象. 研究结果有助于进一步理解非线性各向异性对离散孤子相互作用的影响机制, 并为后续实验研究提供理论参考.     

均匀聚焦磁场中束晕-混沌的孤子控制

采用粒子.束核模型,对均匀聚焦磁场中满足K-V分布的离子束进行模拟研究.观察到束晕.混沌现象,基于束晕.混沌的非线性控制策略,提出控制束晕.混沌的孤子函数控制器,并给出具体的实施方案.模拟研究表明,运用这种方法可以消除束晕及其再生现象,达到对束晕.混沌的有效控制.