论文标题
极端孤子碰撞的统计特性
Statistical properties of extreme soliton collisions
论文作者
论文摘要
在统计描述的背景下，考虑了大量孤子之间的同步碰撞。结果表明，在相同符号的孤子相互作用中，波场有效地平滑了。当孤子的数量增加并且幅度衰减的序列较慢时，聚焦波就变得更加顺畅，并且统计矩很长时间就会被冻结。该准平台状态的特征是大大减少了统计矩和接近某些临界值的孤子的密度。该状态可能被视为小分散极限，这使得可以分析估计所有高阶统计矩的可能性。虽然该研究的重点是在Korteweg--de Vries方程式及其修改版本上，但讨论了结果支持孤子型解决方案的方程的更广泛的适用性。
Synchronous collisions between a large number of solitons are considered in the context of a statistical description. It is shown that during the interaction of solitons of the same signs the wave field is effectively smoothed out. When the number of solitons increases and the sequence of their amplitudes decay slower, the focused wave becomes even smoother and the statistical moments get frozen for a long time. This quasi-stationary state is characterized by greatly reduced statistical moments and by the density of solitons close to some critical value. This state may be treated as the small-dispersion limit, what makes it possible to analytically estimate all high-order statistical moments. While the focus of the study is made on the Korteweg--de Vries equation and its modified version, a much broader applicability of the results to equations that support soliton-type solutions is discussed.
