The KdV soliton crosses a dissipative and dispersive border

英文摘要：

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 passed wave either retains the form of a soliton (though of different parameters) or becomes a bi-soliton. 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 vapour saturation/condensation area. Some rough estimations for a prediction of an output are given using relative decay of the KdV conserved quantities are given. Keywords: KdV- Burgers, non-homogeneous layered media, soliton, bi-soliton, reflection, refraction.