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The KdV soliton crosses a dissipative and dispersive border
Differential Geometry and its Applications ( IF 0.6 ) Pub Date : 2021-01-25 , DOI: 10.1016/j.difgeo.2021.101723
Alexey Samokhin

We demonstrate the behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or dispersion; beyond the layer dispersion is constant (but not necessarily of the same value) and dissipation is null. The transmitted wave either retains the form of a soliton (though of different parameters) or scatters a into a number of them. And a reflection wave may be negligible or absent. This models a situation similar to a light passing from a humid air to a dry one through the vapor saturation/condensation area. Some rough estimations for a prediction of an output are given using the relative decay (or accumulation) of the KdV conserved quantities in a dissipative area; in particular for a restriction for a number of solitons in the transmitted signal.



中文翻译:

KdV孤子穿过耗散和分散的边界

我们证明了孤子的行为,该孤子在非耗散且色散恒定的介质中移动时会遇到具有变化的耗散和/或色散的有限宽度的障碍。超出层的色散是恒定的(但不一定是相同的值),耗散为零。传输的波要么保持孤子的形式(尽管参数不同),要么将a散射成多个。并且反射波可以忽略不计或不存在。这模拟了一种情况,类似于从潮湿的空气通过蒸气饱和/冷凝区域到干燥的空气的光线。使用耗散区域中KdV守恒量的相对衰减(或累加),给出了一些用于输出预测的粗略估计。特别是为了限制发射信号中的孤子数量。

更新日期:2021-01-25
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