飞秒暗孤子间相互作用的数值研究

通过数值模拟对飞秒暗孤子间的相互作用进行了研究，并且同飞秒亮孤子和皮秒暗孤子分别进行了比较，结果表明：同飞秒亮孤子相比，飞秒暗孤子间的相互作用比较小，前者表现为相互吸引、碰撞、合二为一，然后相互排斥，不具有周期性；而后者从一开始就相互排斥，且这种排斥作用较亮孤子来说相当微弱，同样也不具有周期性。此外，数值模拟的结果还表明，飞秒暗孤子间的相互作用同皮秒尺度下暗孤子间的相互作用基本一致，并且通过计算表明，飞秒暗孤子间的相互作用在一定范围内仍可利用皮秒尺度下暗孤子间相互作用的经验公式。但是，数值模拟结果显示，两孤子的初始间距越小，由经验公式计算结果所带来的误差就越大。

Numerical Research of Interactions Between Femtosecond Dark Solitons

The interactions between two femtosecond dark solitons are numerically investigated. The results show that femtosecond dark solitons are less affected than bright solitons by their respective interaction forces. The latter attracts each other and collides into one pulse, then they keep the state of repulsion without periodicity. The former repulses all the way and the repulsive forces are weaker than those of bright solitons. They have no periodicity,either. In addition,the numerical simulation results show that the interactions between femtosecond dark solitons are the same as those of picosecond dark solitons. It is found that their interactions agree with the empirical expression of picosecond dark solitons for the separation of two solitons as a function of initial separation and traveling distance. And the smaller the initial separation between two dark solitons is, the larger the difference between numerical simulation results and formula calculation results is.