Shocks and Solitons in Ultradense Degenerate Electron-Positron-Ion Plasmas

The formation and propagation of shocks and solitons are investigated in anunmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger (dKdVB) equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar (cylindrical and spherical) geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.     

HBK方程的达布变换及其孤子解

孤子方程是非线性科学领域中很有潜力的研究课题。根据HBK方程的Lax对,借助HBK方程的谱问题和规范变换,构造出一个含多参数的达布变换。通过此变换,最终求得HBK方程的孤子解,并且讨论了N=1和N=2两种孤子解的情况。     

球对称非谐势阱中玻色-爱因斯坦凝聚Gross-Pitaevskii方程的精确解

考虑了描述玻色 爱因斯坦凝聚的Gross-Pitaevskii(GP)方程, 得到了在球对称非谐势阱中玻色-爱因斯坦凝聚GP方程的精确亮孤子解。In this paper, we analyze Gross Pitaevskii equation which describes the dynamics of a bright soliton in trapped atomic Bose Einstein condensates, and obtain the exact bright soliton solution of Gross Pitaevskii equation in spherically symmetric non harmonic trap.     

广义Kuramoto-Sivashinsky方程的孤子解

孤立子的高度稳定性和粒子性引起了人们对孤立子的极大兴趣,并且在流体物理、固体物理、等离子体物理和光学实验中频频被发现,很多非线性发展方程都存在孤立子解。在符号计算的帮助下,利用tanh-函数方法,得到广义Kuramoto-Sivashinsky方程的新的更广义类型的孤子解,此方法还可被应用到其它非线性发展方程中去。 更多还原     

Polarization-dependent efficient Cherenkov radiation at visible wavelengths in hollow-core photonic crystal fiber cladding

Efficient Cherenkov radiation (CR) is experimentally generated by a soliton self-frequency shift (SSFS) in a knot of hollow-core photonic crystal fiber (HC-PCF). When the angle of the half-wave plate is rotated from 0° to 45° , the Raman soliton shifts from 2227 to 2300 nm, the output power of the CR increases 8.15 times, and the maximum output power ratio of the CR at 556 nm to the residual pump is estimated to be 20:1. The width of the output optical spectrum at visible wavelengths broadens from 25 to 45 nm, and the conversion efficiency of the CR can be above 28%. Moreover, the influences of the pump polarization and wavelength on the CR are studied, and the corresponding nonlinear processes are discussed.     

异核两组分玻色-爱因斯坦凝聚体中暗孤子的形成及其性质

数值模拟准一维异核两组分玻色-爱因斯坦凝聚体在谐振子势阱中的运动,研究调制不稳定性条件(MI条件)下暗孤子的形成及其性质.在调制不稳定性条件下,凝聚体基态形成后,瞬间使组分间的相互排斥力变为相互吸引力,实时演化可以形成暗孤子.对各组分自身相互作用系数分析发现,它们之间满足一定关系时暗孤子在不同的组分内形成,而且形成的暗孤子在谐振子势阱中呈现周期性的往返对穿运动.讨论了形成暗孤子数目与两种粒子的质量比率和粒子数比率存在的关系.     

一种改善损耗光纤中皮秒脉冲孤子效应压缩效果的方法

以常规光纤中的皮秒脉冲孤子效应压缩过程为基础,研究了在有无损耗的光纤中初始啁啾对脉冲压缩的影响。研究发现,在损耗光纤中引入初始啁啾能够抵消光纤损耗对孤子效应压缩的负面影响,从而大大改善了脉冲压缩的效果。如果所选取的啁啾值适当,则可以几乎完全抵消光纤损耗的作用,从而使光脉冲呈现出如同在无损耗的光纤中传输时一样。     

损耗色散管理光纤中类明孤子传输特性的数值模拟研究

对有损耗的色散光纤中光波包络的非线性方程进行变换,借助数学软件得到非线性方程的数值曲线,并通过对曲线的拟合得到方程的近似解,对色散管理类明孤子的传输进行了分析．     

(2+1)维广义浅水波方程类孤子解和类周期解

在Riccati方程方法的基础上提出了新的广义投射Riccati方程展开法及其算法.该方法直接而有效,通过适当的变换将非线性发展方程转化为易于求解的微分方程组,从而可用来构造非线性发展方程更多新的精确解.利用这个方法研究了(2 1)维浅水波方程,并得到了许多新的精确解,其中包括类孤子解和类周期解.该算法可以用于构造其他更多非线性发展方程(组)的精确解.     

Effect of the third-order filter term on soliton interactions in soliton transmission systems with filters

The effect of the third-order filter term on soliton interactions in optical fibers with guiding filters is theoretically analyzed. We find that this term causes a significant difference to the interaction of solitons through filters among the regimes of without sliding, with up- and down-sliding frequencies of filters. It is shown that the interaction between solitons can be more effectively suppressed by up-sliding filters than that by down-sliding filters in the presence of the third-order filter term. Moreover, the third-order filter term is found to play a positive role in suppressing soliton interactions in the case of non-sliding.