参数可变强非局域非线性介质中球贝塞尔孤立波

Spherical Bessel Solitary Waves in Strongly Non-local Nonlinear Media with Variable Parameters

研究了具有参数可变强非局域非线性效应的玻色-爱因斯坦凝聚中物质波的演化。首次获得参数可变系统中三维强非局域Gross-Pitaevskii方程的解析解即自相似球贝塞尔孤立波解。存在于强非局域非线性相互作用能的BEC中的物质波强度即粒子数密度的径向呈球贝塞尔函数分布,角向呈球谐函数分布,且波强随自相似变量的变化关系不随演化时间而改变。物质波具有线性相位和空间啁啾。

The evolution of matter waves in Bose-Einstein condensations with both strong non-local nonlinear effects and variable parameters is studied. For the first time, the self-similar spherical Bessel solitary wave solution of the three-dimensional strongly non-local Gross-Pitaevskii equation with variable parameters is obtained. The intensity of matter wave existing in the BEC with strong non-local nonlinear interaction energy, namely the particle number density, is distributed in the radial direction as a spherical Bessel function, and in the angular direction as a spherical harmonic function. The wave intensity varies with self-similar variables, however,does not change with evolution time. Such a matter wave has linear phase and spatial chirp.