Dispersion management (B02)

色散管理技术已经导致光缆中可能的数据传输速率的巨大增长。它基于沿电缆的色散的强烈局部变化，具有很小的平均色散甚至零平均色散。尽管物理文献中有许多结果，但到目前为止，人们只用严格的数学方法展示了相应的演化方程及其驻波--DM孤子的几个基本性质。我们研究了DM-孤子的唯一性(模自然不变性)和对称性、渐近稳定性、最小能量的DM-孤子是否高度振荡以及是否存在反对称的高能DM-孤子等问题。

The dispersion management technique has led to an enormous growth in the possible data transfer rate in optical cables. It is based on a strong local variation of the dispersion along the cable with a small or even zero average dispersion. Despite many results in the physics literature, in a mathematical rigorous way so far one has shown only a few basic properties of the corresponding evolution equation and their standing waves, the DM-solitons. We study important open questions such as uniqueness (modulo natural invariances) and symmetry of the DM-solitons, their asymptotic stability, whether DM-solitons of minimal energy are highly oscillating and whether anti-symmetric ones of higher energy exist.