微扰Burgers-KdV方程的孤子解

对于一个其耗散项可看作微扰的Burgers-KdV(B-KdV)方程u_t+uu_x+βu_xxx=εu_xx,|ε|?1,考虑一级近似和行波情形,建立一套求通解的直接扰动方法,利用零级方程的单孤子解,获得一级方程的孤子型通解,它包含任意多个不同的孤子解,每个孤子解分别描述一个位于半无限空间的孤子阵列,分析表明,耗散使得“亮孤子”变矮变窄,“暗孤子”变浅变窄. 关键词：     

控制离子云混沌运动中的不稳定性

射频阱中离子云与检测场的相互作用由Dufing方程描述．在小阻尼条件下，得到嵌于混沌吸引子中的不稳定周期解及其稳定性条件．分析表明，调节直流扫描电压等参数去拟合该条件，可以控制混沌运动中的不稳定性．有关实验定性支持这一结论． 关键词：     

MAXIMAL EMITTED POWER OF HYPERRADIANCE FROM PERTURBED JOSEPHSON SYSTEMS

Consider two magnetically coupled and perturbed long Josephson junctions which operate in synchronized modes. Under first order approximation, the soliton solution of the system is derived by using a new perturbation technique. It is shown that the perturbing parameters limit the emitted power from the system, and the physically relevant coupling parameter leads to the increase of power. The formula of maximal emitted power is given for a particular power input. The results solve some important problems left over by previous analysis.     

双δ激光脉冲作用下Paul阱中单离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与双δ脉冲型周期势相互作用系统的规则与混沌运动.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道图和平均能量的时间演化曲线.结合分析与数值结果,发现两个有趣的结论.即在离子与单δ脉冲作用出现共振失稳的情形,在双δ脉冲作用下却出现了稳定的规则运动;离子随着双δ脉冲中两个脉冲之间的时间间隔减小而由规则运动转为混沌运动,其平均能量扩散的快慢与混沌运动的混乱程度相关.还研究了系统的共振失稳,发现通过调节激光波矢可以控制这种不稳定性.     

Boundedness and convergence of perturbed corrections for helium-like ions in ground states

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.     

无反射势阱的非齐次Schr(o)dinger方程的精确解

无反射势阱描述一种双原子分子的吸引势。将Ｒａｙｌｅｉｇｈ－Ｓｃｈｒｏｄｉｎｇｅｒ展开法应用到微扰无反射势阱,得以一组非齐次Ｓｃｈｒｏｄｉｎｇｅｒ方程。利用最近报道的微扰方法,导出这些方程的积分形式的精确解。以静电场与基态系统的相互作用为例,通过精确解的有界及其不能在Ｈｉｌｂｅｒｔ空间展开为有限项的性质,论证了该微扰系统束缚态的存在性及通常量子力学发散困难的起因。     

Nonautonomous deformed solitons in a Bose-Einstein condensate

We study exact single-soliton solutions of an attractive Bose-Einstein condensate governed by a one-dimensional nonautonomous Gross-Pitaevskii system. For several different forms of time-dependent atom-atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton＇s center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.     

双δ激光脉冲作用下Paul阱中单离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与双δ脉冲型周期势相互作用系统的规则与混沌运动.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道图和平均能量的时间演化曲线.结合分析与数值结果,发现两个有趣的结论.即在离子与单δ脉冲作用出现共振失稳的情形,在双δ脉冲作用下却出现了稳定的规则运动;离子随着双δ脉冲中两个脉冲之间的时间间隔减小而由规则运动转为混沌运动,其平均能量扩散的快慢与混沌运动的混乱程度相关.还研究了系统的共振失稳,发现通过 关键词： 双δ脉冲 囚禁离子 精确解 混沌     

GENERAL SOLITON SOLUTIONS OF THE COUPLED SCALAR FIELDS

Let σ and ρ be two field variables of the n-dimensional coupled scalar fields. Taking the function transformations σ=σ(ξ) and ρ=ρ(ξ) leads to an equation F(σ,ρ,dσ/dρ,d²σ/d²ρ) =0. Inserting any solution of this equation into the field equations yields a pair of general soliton solutions σ=σ(ξ) and ρ=ρ[σ(ξ)]. Some interesting specific soliton solutions are given. The stability and other properties of these solitons are discussed.     

无反射势阱的非齐次Schrdinger方程的精确解

无反射势阱描述一种双原子分子的吸引势。将Rayleigh Schr dinger展开法应用到微扰无反射势阱 ,得到一组非齐次Schr dinger方程。利用最近报道的微扰方法 ,导出这些方程的积分形式的精确解。以静电场与基态系统的相互作用为例 ,通过精确解的有界及其不能在Hilbert空间展开为有限项的性质 ,论证了该微扰系统束缚态的存在性及通常量子力学发散困难的起因。