Solitons in quadratic media
Solitons in quadratic media
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二次介质中的孤子
DOI：
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发表时间：
2016
期刊：
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通讯作者：
J. Saut
中科院分区：
文献类型：
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作者：
M. Colin;L. Menza;J. Saut
在本文中，我们研究了二次介质中出现的孤子结构的性质。首先，我们回顾了控制在此类介质中传播的波的相互作用过程的系统的推导，并检查相应柯西问题的局部和全局适定性。然后，我们在正常或反常色散体系的背景下寻找稳态，这导致我们得到椭圆或非椭圆系统，并解决轨道稳定性问题。最后，进行了一些数值实验，以计算几种状态的局域状态并研究动态稳定性以及长时间渐近。
In this paper, we investigate the properties of solitonic structures arising in quadratic media. First, we recall the derivation of systems governing the interaction process for waves propagating in such media and we check the local and global well-posedness of the corresponding Cauchy problem. Then, we look for stationary states in the context of normal or anomalous dispersion regimes, that lead us to either elliptic or non-elliptic systems and we address the problem of orbital stability. Finally, some numerical experiments are carried out in order to compute localized states for several regimes and to study dynamic stability as well as long-time asymptotics.