Bi-solitons, breather solution family and rogue waves for the (2+1)-dimensional nonlinear Schr\"{o}dinger equation

In this paper, bi-solitons, breather solution family and rogue waves for the (2+1)-Dimensional nonlinear Schr\"{o}dinger equations are obtained by using Exp-function method. These solutions derived from one unified formula which is solution of the standard (1+1) dimension nonlinear Schr\"{o}dinger equation. Further, based on the solution obtained by other authors, higher-order rational rogue wave solution are obtained by using the similarity transformation. These results greatly enriched the diversity of wave structures for the (2+1)-dimensional nonlinear Schr\"{o}dinger equations     

双色激光场中激光强度和脉宽对线性多原子分子离子电离的影响

 利用强激光场电离和离解分子来研究分子激发态的波包结构是强场物理的重要研究方向。利用短时指数传播子对称分割法和快速傅里叶变换技术,数值求解了一维含时Schr-dinger方程,探讨了双色激光场中激光的基波和谐波强度之间的不同配比以及脉宽对线性多原子分子离子电离的影响。理论计算结果表明：基波和谐波的相对相位为π时,尽管随着激光的基波和谐波强度之间配比的变化,电离几率随原子间距变化的趋势基本保持不变,但在一定的激光基波强度下（1.2×10¹³~1.2×10¹⁵ W/cm²),激光基波强度的变化可以明显改变电离几率随原子间距变化的趋势。另外,激光脉冲的持续作用可以增强分子的电离,取原子个数为5,基频光波长为800 nm,基波与谐波的强度配比为4,频率配比为2,当其作用时间达到75 fs时,电离基本接近饱和。采用外静电场电离模型能够合理地解释这些现象。     

Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated with magnetic Schr?dinger operators

Let φ be a growth function, and let A:=-(?-ia)?(?-ia)+V be a magnetic Schr?dinger operator on L2(?n),n≥2, where α:=(α1,α2,?,αn)∈Lloc2(?n,?n) and 0≤V∈Lloc1(?n). We establish the equivalent characterizations of the Musielak-Orlicz-Hardy space HA,φ(?n), defined by the Lusin area function associated with {e-t2A}t>0, in terms of the Lusin area function associated with {e-tA}t>0, the radial maximal functions and the nontangential maximal functions associated with {e-t2A}t>0 and {e-tA}t>0, respectively. The boundedness of the Riesz transforms LkA-1/2,k∈{1,2,?,n}, from HA,φ(?n) to Lφ(?n) is also presented, where L_k is the closure of ??xk-iαk in L2(?n). These results are new even when φ(x,t):=ω(x)tp for all x∈?nand t ∈(0,+∞) with p ∈(0, 1] and ω∈A∞(?n) (the class of Muckenhoupt weights on ?n).     

On perturbation theory for an asymmetric anharmonic oscillator

A modified perturbation theory is formulated for an asymmetric anharmonic oscillator based on a choice of the main approximation constructed by analogy with the self-consistent field model. This perturbation theory has a much wider range of application in comparison with the standard approach and considers a finite number of energy levels in the potential well already in the main approximation. This approach is used for the construction of a two-atomic model of a quantum crystal. A quantum analog of the Lindeman criterion is obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 30–40, January, 2009.     

数值求解三维含时Schr?dinger方程及其应用

发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrdinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高. 关键词： 三维含时Schrdinger方程 库仑奇点 强场 含时波包传播     

Generalized Harmonic Oscillator and the SchrSdinger Equation with Position-Dependent Mass

We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties corresponding effective potentials for several mass functions, for the system with PDM are also discussed. We give the the systems with such potentials are isospectral to the usual harmonic oscillator.     

Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability

Theoretical and Mathematical Physics - A correspondence between the families of generalized nonlinear Schrödinger (NLS) equations and generalized KdV equations was recently found using a...     

非齐次光纤介质中非线性薛定谔方程的相似变换与精确解

基于李群理论和符号计算, 获得了具有增益/损耗项和频率啁啾项的非齐次光纤介质中的非线性薛定谔方程的相似变换; 利用所得变换, 把具有群速度参数、克尔非线性效应参数、相位调制参数和增益/损耗参数的变系数非线性薛定谔方程约化为相应常系数非线性薛定谔方程. 通过一个广义的直接求解方法, 构造了常系数非线性薛定谔方程的一组亮孤子解和一组暗孤子解, 进而得到了变系数非线性薛定谔方程丰富的精确解. 最后对所得亮孤子解和暗孤子解进行了动力学分析与讨论.     

A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.