中文摘要：

介绍了广义非线性薛定谔方程,并且运用分步傅里叶方法进行了数值求解.在外部势场一定的情况下,给定系统一个小的初始扰动,讨论了广义非线性薛定谔方程中复系数p,q对波场演变过程的影响.通过数值研究发现波场会相继出现调制不稳定性、波坍缩、逆级联以及整个空间的湍流现象.而当改变非线性频移系数的量级时,数值研究发现在波坍缩之后出现了逆级联,最终系统的能量主要凝聚在3个不同波矢终端的附近区域.

英文摘要：

A generalized nonlinear Schrodinger equation is numerically studied using the split-step Fourier method. For a fixed external potential field and an initial pulse disturbance, the effects of the complex coefficients p and q in the nonlinear Scbrodinger equation on the evolution of the wave field are investigated. From a large number of simulations, it is found that the evolution of the wave field remains similar for different signs of the real parts of p and q, and different values of the real part of p. The initial pulse consisting of the longest wavelength modes （in the smallest-丨k丨 corner of the phase space） of the spectrum first suffers modulational instability. Collapse begins at t ～ 0.1, followed by inverse cascade of the shortest wavelength modes to longer wavelength ones, so that the whole k space becomes turbulent. For p = 1 ＋ 0.04i, and q = 1 ＋ 0.6i, it is found that first modulational instability occurs in the longer wavelength regime and the wave energy is transferred to the larger 丨k丨 modes. Then the wave collapse appears with increasing wave energy. Next, the large-丨k丨 modes condense into a smaller-丨k丨 mode by inverse cascade before spreading to the center of the phase space, until a turbulent state occurs there. Finally, most of the wave energy is condensed to the neighborhoods of three modes.