(2+1)维扰动时滞破裂孤波方程行波解的摄动方法

研究了一类(2+1)维扰动时滞破裂孤波方程. 首先讨论了对应的无时滞情形下的破裂方程,利用待定系数投射方法得到了孤波精确解. 再利用同伦、摄动近似方法得到了扰动破裂孤波方程的行波渐近解. 关键词： 孤波 行波解 近似解     

二次型径向折射率和增益分布介质中高阶高斯光束模式的严格解析解

本文在缓变波包络近似(SVEA)下导出了具有二次型径向折射率和增益(损耗)分布介质中高阶高斯光速传播波模的严格一般解析解和和稳态解.给出了几种常用特殊情形的一般解和稳态解的显示表式.讨论了本理论在具有这类介质光学谐振腔、光波导和光学双稳器件中的可能应用.     

四波混频泵浦消耗过程的相位匹配条件研究

采用解析方法分析讨论泵浦消耗情形下的准相位匹配范围以及相位匹配条件的变化,并给出相位匹配条件的表达式.比较分析小信号近似和泵浦消耗两种情形下四波混频增益演化过程.研究表明,在泵浦消耗情形下,随转移功率的增大,满足总相位匹配的线性失配因子从负值逐渐趋于0,准相位匹配范围也越来越小;确定四波混频的准相位匹配范围,可简化波分复用或空分复用系统中级联四波混频的分析过程;小信号近似模型只适合于转移功率远小于泵浦功率的情形,满足总相位匹配的线性失配因子不依赖于光纤长度.     

一类尘埃等离子体孤波解

研究了一类非线性尘埃等离子体孤波解.首先对无扰动情形下的孤波解作了阐述,接着用同伦映射方法,构造了一个迭代,并求出到了非线性尘埃等离子体扰动单孤波的行波解.最后得到了对应模型的单孤波的各次近似解.     

一般匀强电磁场中电荷的相对论性运动

将电荷在匀强电磁场中的运动从电磁场正交推广到非正交的一般情形,且在相对论情形下进行了一般讨论.然后将一般结果用于初始时静止的电荷,得到其运动学方程,并讨论了各种特殊情况,包括两种非相对论近似及对应的相对论修正.     

不可压N-S方程的基于粘接元的区域分裂解法

首先,简单介绍了基于粘接元的无重叠区域分裂方法.这种方法利用变分原理,非常适合有限元近似.然后,着重讨论了这种区域分裂方法在求解不可压Navier-Stokes方程中的应用,具体包括等价变分公式的建立、通过算子分裂的时间离散、区域分裂情形下广义Stokes问题的共轭梯度迭代求解方法、空间的有限元离散.最后,以数值实验结果验证了这种区域分裂方法应用于不可压Navier-Stokes方程求解时的可靠性.     

不变本征算符法计算各向异性海森伯亚铁磁系统的自旋波能量

利用不变本征算符法计算了X-Y-Z模型各向异性海森伯亚铁磁系统的自旋波能量,并讨论了此系统特殊情形下的自旋波能量及不变本征算符法的优点与不足.     

薛定谔扰动耦合系统孤波的行波近似解法

研究了一类薛定谔非线性耦合系统.利用精确解与近似解相关联的特殊技巧,首先讨论了对应的无扰动耦合系统,利用投射法得到了精确的孤波解.再利用泛函映射方法得到了薛定谔非线性扰动耦合系统的行波近似解.     

厄尔尼诺大气物理机理的变分迭代解法

研究了一个厄尔尼诺大气物理机理振荡.利用变分迭代理论，简捷地得到了该模型解的近似展开式.通过与特殊情形下模型的精确解的比较，得到的一次近似解具有完全符合的精确度. 关键词： 非线性 变分迭代 厄尔尼诺现象     

(e,2e)反应中冲量近似的理论研究

利用冲量近似理论和玻恩近似方法, 以氢原子(1s)为例, 在共面不对称几何条件下用多种模型分别计算了若干入射能、 散射角情形下电子碰撞电离(e, 2e) 反应的三重微分散射截面. 与其他的理论方法和实验数据进行了比较, 分析了曲线结构差异及原因, 对其适用范围进行了研究, 并探讨了交换效应的贡献, 验证了早期的研究. 关键词： 扭曲波冲量近似 平面波冲量近似 三重微分截面     

CONNECTION THEORY OF FIBRE BUNDLE AND PROLONGATION STRUCTURES OF NONLINEAR EVOLUTION EQUATIONS

It is shown that the proper geometrical framework for the nonlinear evolution equations (NEEs) and the soliton equations Should be the fibre bundle theory, the principal bundle and its associated bundle and their connection theory. Based upon the requirement of covariance of the geometrical quantities, a covariant generic geometry theory for the prolongation strutures of the NEEs is proposed and the fundamental equations for the prolongation structures are presented. From the fundamental equations it immediately follows that the comections corresponding to these NEEs always flat but with torsion and the covariant formulae satisfied by the conservation quantities associated with these NEEs are obtained. The prolongation structure of the MKdV equation, as an example, is concretely worked out by means of the covariant theory of the prolongation structure presented in this paper.     

A New Modified Extended Tanh-Function Method and Its Application

In this paper, a new modified extended tanh-function method is presented for constructing soliton-like,periodic form solutions of nonlinear evolution equation (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Lett. A277 (2000) 212] and the moditied extended tanh-function method [Phys. Lett. A285(2001) 355]. Abundant new solutions of two physically important NEEs are obtained by using this method and symbolic computation system Maple.     

New Method for Finding a Series of Exact Solutions to Generalized Breaking Soliton Equation

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like,period-form solutions of nonlinear evolution equations (NEEs). This method is more powerful than the extended tanhfunction method [Phys. Left. A 277 (2000) 212] and the modified extended tanh-function method [Phys. Left. A 285 (2001) 355]. Abundant new families of the exact solutions of Bogoyavlenskii‘s generalized breaking soliton equation are obtained by using this method and symbolic computation system Maple.     

Direct Similarity Solution Method and Comparison with the Classical Lie Symmetry Solutions

Abstract

We study the general applicability of the Clarkson–Kruskal’s direct method, which is known to be related to symmetry reduction methods, for the similarity solutions of nonlinear evolution equations (NEEs). We give a theorem that will, when satisfied, immediately simplify the reduction procedure or ansatz before performing any explicit reduction expansions. We shall apply the method to both scalar and vector NEEs in either 1+1 or 2+1 dimensions, including in particular, a variable coefficient KdV equation and the 2+1 dimensional Khokhlov–Zabolotskaya equation. Explicit solutions that are beyond the classical Lie symmetry method are obtained, with comparison discussed in this connection.     

构造非线性发展方程无穷序列复合型精确解的一种方法

为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Bäcklund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义. 关键词： 非线性发展方程 非线性叠加公式 Riccati方程 无穷序列精确解     

高斯光束在对数型非线性介质中自诱导效应

从标量Helmholtz方程出发,推导了对数饱和非线性介质中光场满足的非线性Schr dinger方程(NLSE)。通过与梯度折射率下的光场满足的方程比较,发现高斯光束在对数型饱和非线性介质中可自诱导梯度折射率。利用数值计算,详细地讨论了自诱导梯度折射率对高斯光束传输特性的影响。发现高斯光束在其自诱导的梯度折射率的影响下,呈振荡形式的准稳定的传输。光束注入介质中的初始状态,直接影响着光束的振荡形式(先发散还是先聚焦)、振荡深度(幅度)、振荡周期。得到高斯光束形成孤子的条件,以及若使高斯光束在对数饱和非线性介质中保持小损耗、高稳定的传输,应该使光束在阈值(孤子条件)附近注入介质的结论。     

多轴差分吸收光谱技术反演气溶胶消光系数垂直廓线

研究了多轴差分吸收光谱技术(MAX-DOAS)的气溶胶消光系数垂直廓线反演算法. 该算法应用非线性最优估算法, 通过MAX-DOAS测量的氧的二聚体(O₄), 反演气溶胶消光系数垂直廓线和光学厚度(AOD). 首先研究了非线性最优估算法中权重函数、先验廓线协方差矩阵、测量不确定度协方差矩阵的计算方法, 针对中国气溶胶浓度较高且变化剧烈的特征, 设计了非线性迭代方案. 然后在低气溶胶、高气溶胶和抬高型气溶胶三种状态下, 通过计算机仿真模拟验证了MAX-DOAS气溶胶消光系数垂直分布反演算法, 讨论了误差来源. 之后在合肥地区开展了连续观测实验, 并将反演的AOD与CE318太阳光度计对比, 两者的相关性系数达到了0.94. AOD反演的相对误差约为20%. 又将反演的最低层(0–0.3 km)气溶胶消光系数与能见度仪对比, 两者的相关性系数为0.65. 近地面气溶胶消光系数反演的总相对误差约为10%. 模拟验证和对比实验均说明本文研究的气溶胶消光系数垂直廓线反演算法可以较好地获取对流层的气溶胶状态. 关键词： 多轴差分吸收光谱 气溶胶消光系数垂直廓线 气溶胶光学厚度 最优估算法     

Rayleigh wave at the boundary of an inhomogeneous nonlinear viscoelastic half-space

In the approximation of weak nonlinearity and weak viscosity of the medium, we obtain an equation describing the spectral density of the particle horizontal velocity for a Rayleigh wave propagating along the boundary of a half-space. The coefficients of nonlinear interaction between the wave harmonics are found on the assumption that the third-order elastic moduli arbitrarily depend on the depth. We find expressions for the complex correction to the wave frequency due to small relaxation corrections to the elastic moduli and small variations in the medium density, which arbitrarily depend on the depth as well. The imaginary part of this correction to the frequency determines the decay of the linear Rayleigh wave due to small relaxation corrections to the elastic moduli arbitrarily dependent on the depth. Using numerical simulation (with allowance for the interaction of 500 harmonics), we study distortions of an initially harmonic Rayleigh wave for a particular dependence of variations in the nonlinear moduli on the depth. An integral equation is derived for the nonlinear elastic moduli as functions of the depth. It is shown that for independent spatio-temporal distributions of the viscous moduli, functions determining the dependence of the viscosity on the depth are described by an analogous integral equation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 3, pp. 212–226, March 2007.     

Rogue waves in the basin of intermediate depth and the possibility of their formation due to the modulational instability

The properties of rogue waves in the basin of intermediate depth are discussed in comparison with known properties of rogue waves in deep waters. Based on observations of rogue waves in the ocean of intermediate depth we demonstrate that the modulational instability can still play a significant role in their formation for basins of 20 m and larger depth. For basins of smaller depth, the influence of modulational instability is less probable. By using the rational solutions of the nonlinear Schrodinger equation (breathers), it is shown that the rogue wave packet becomes wider and contains more individual waves in intermediate rather than in deep waters, which is also confirmed by observations.     

基于铋可饱和吸收体的超快激光产生

采用磁控溅射沉积法在微纳光纤表面上镀一层纳米级厚度的铋薄膜,制备了一种微纳光纤-铋膜结构的可饱和吸收体.在1.5μm处的非线性光调制深度为14%.将其应用到掺铒光纤激光器中,在1.5μm波段获得稳定的超快脉冲激光产生,脉宽为357 fs,输出功率为45.4 mW,单脉冲能量为2.39 nJ,信噪比为84 dB.实验结果表明,利用磁控溅射法可制备出大调制深度的可饱和吸收体,为获得高能量超短脉冲激光输出提供新方案.