论文标题
Korteweg -de Vries方程中孤子同步碰撞的属性
Properties of synchronous collisions of solitons in the Korteweg - de Vries equation
论文作者
论文摘要
Korteweg孤子的同步碰撞 - De Vries方程被认为是孤子气中大量孤子相互作用的代表性示例。根据功率定律检查了孤子场的统计特性，以了解孤子幅度的模型分布。 $ n $ -soliton解决方案（$ n \ le 50 $）是在使用Darboux转换和100位数算术的数值过程的帮助下构建的。结果表明，根据振幅分布，在定性上存在不同的模式。大量孤子的碰撞导致统计矩值的减少（已经考虑了3个命令）。在有足够数量的具有近距离振幅的相互作用的孤子子的情况下，统计矩显示出很长的准平台行为间隔。这些间隔可以以孤子气体密度的最大值和在整体意义上的“平滑”为特征。得出了描述这些相互作用孤子的堕落状态的分析估计。
Synchronous collisions of solitons of the Korteweg -- de Vries equation are considered as a representative example of the interaction of a large number of solitons in a soliton gas. Statistical properties of the soliton field are examined for a model distribution of soliton amplitudes according to a power law. $N$-soliton solutions ($N \le 50$) are constructed with the help of a numerical procedure using the Darboux transformation and 100-digits arithmetic. It is shown that there exist qualitatively different patterns of evolving multisoliton solutions depending on the amplitude distribution. Collisions of a large number of solitons lead to the decrease of values of statistical moments (the orders from 3 to 7 have been considered). The statistical moments are shown to exhibit long intervals of quasi-stationary behavior in the case of a sufficiently large number of interacting solitons with close amplitudes. These intervals can be characterized by the maximum value of the soliton gas density and by ``smoothing'' of the wave fields in integral sense. The analytical estimates describing these degenerate states of interacting solitons are obtained.
