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Stability analysis of a solitary wave solution in dispersive linear media

机译：色散线性介质中孤波解的稳定性分析

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Optical solitons, particularly solitary waves, which preserve their shape and energy as they propagate through a medium, have attracted considerable attention because of their potential applications to ultra-high bit-rate optical communications and ultrafast signal-routing systems. So far, most of the researches on optical solitons are still focused on the case, in which either the transverse confinement or the dispersion effect is investigated under an independent manner (i.e., temporal or spatial envelope optical solitons). However, with the great advance in experiment techniques, the short and intense femto-second optical pulses in solid-state lasers can easily be produced. Therefore, it is necessary to investigate the transmission properties of-optical pulses under the combined effects of transverse confinement and group velocity dispersion, Some analytical and numerical researches on the time-space coupled higher-dimensional wave equation have been made under the above-mentioned combined effects condition. On the other hand, it should be noted that one of the reasons of investigating the transmission of optical pulses in a nonlinear medium is that no solitary wave solution had been discovered in a dispersive linear medium until recently we proved, for the first time to our knowledge, that an envelope solitary wave solution may exist even in a dipersive linear medium under certain appropriate conditions by taking into account the transverse effect and dispersion effect simultaneously. This may open a new way of realizing very high bit-rate optical communications. However, the stability of the solution in ref [10] remains an open question.
机译：光孤子，尤其是孤波，在通过介质传播时保持其形状和能量，因此受到了极大的关注，因为它们潜在地应用于超高比特率光通信和超快信号路由系统。迄今为止，关于光孤子的大多数研究仍集中在以独立方式（即时间或空间包络光孤子）研究横向限制或色散效应的情况。但是，随着实验技术的飞跃发展，可以轻松地产生固态激光器中短而强的飞秒光脉冲。因此，有必要研究横向约束和群速度色散共同作用下光脉冲的传输特性，在上述情况下对时空耦合高维波动方程进行了一些分析和数值研究。联合效应条件。另一方面，应该指出的是，研究非线性介质中光脉冲传输的原因之一是直到最近我们首次证明了在色散线性介质中没有发现孤波解。众所周知，通过同时考虑横向效应和色散效应，即使在一定条件下的浸入线性介质中也可能存在包络孤波解。这可能为实现非常高的比特率光通信开辟了一条新途径。但是，参考文献[10]中解决方案的稳定性仍然是一个悬而未决的问题。

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