Barashenkov-Bogdan-Zhanlav孤子及其稳定性
On the Barashenkov-Bogdan-Zhanlav solitons and their stability
摘要：
研究了强迫NLS/Lugiato-Lefever模型在直线上的Barashenkov-Bogdan-Zhanlav孤子$u_\pm$.虽然$u_+$的不稳定性是在原始论文\cite{B1}中建立的，但对于$u_-$的类似问题仅在理论上和数值上进行了考虑。我们严格地分析了$u_-$在各种参数下的稳定性。特别是，我们表明，$u_-$是光谱稳定的小泵浦强度$h$。此外，$u_-$保持光谱稳定，直到一对中性本征值的负Krein签名击中另一对本征值，这已经从边缘发出的连续谱，\cite{B1, BBK, ABP}。在碰撞后，不稳定性是在以前的作品，\cite{B1}，数值观察和描述。
英文摘要：
The Barashenkov-Bogdan-Zhanlav solitons $u_\pm$ for the forced NLS/Lugiato-Lefever model on the line are considered. While the instability of $u_+$ was established in the original paper, \cite{B1}, the analogous question for $u_-$ was only considered heuristically and numerically. We rigorously analyze the stability of $u_-$ in the various regime of the parameters. In particular, we show that $u_-$ is spectrally stable for small pump strength $h$. Moreover, $u_-$ remains spectrally stable until a pair of neutral eigenvalues of negative Krein signature hits another pair of eigenvalues, which has emanated from the edge of the continuous spectrum, \cite{B1, BBK, ABP}. After the collision, an instability is conjectured and numerically observed in previous works, \cite{B1}.
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