论文标题
在Barashenkov-Bogdan-Zhanlav唯一及其稳定性上
On the Barashenkov-Bogdan-Zhanlav solitons and their stability
论文作者
论文摘要
该产品线上的Barashenkov-Bogdan-Zhanlav solitons $ u_ \ pm $用于强制NLS/Lugiato-Lefever模型。虽然$ u _+$的不稳定性是在原始论文中建立的\ cite {b1}，但$ u _- $的类似问题仅在启发式上和数字上被视为。我们严格地分析了参数的各种策略中$ u _- $的稳定性。特别是，我们表明$ u _- $对于小泵强度$ h $是频谱稳定的。此外，$ u _- $在光谱上保持稳定，直到一对负角质签名的一对中性特征值击中了另一对特征值，该值是从连续频谱的边缘散发出来的，\ cite \ cite {b1，bbk，abp}。碰撞后，在先前的作品中猜想并观察到不稳定性，\ cite {b1}。
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}.
