标题： 驱动阻尼非线性薛定谔孤子的存在阈值 显示英文标题

标题： Existence threshold for the ac-driven damped nonlinear Schrödinger solitons

摘要： 众所周知，对外部驱动、阻尼非线性薛定谔方程的孤立子来说，只有当驱动强度$h$超过大约$(2/ \pi) \gamma$时才能存在，其中$\gamma$是耗散系数。 尽管这一微扰结果被认为仅在$\gamma$的领先阶次下是正确的，但最近的研究表明，公式$h_{thr}= (2 /\pi) \gamma$对孤立子的存在阈值给出了非常准确的描述，这引发了人们认为该公式实际上是精确的猜测。 在本说明中，我们计算了$h_{thr}(\gamma)$展开的下一个阶次，表明这一现象的实际原因是下一个阶次的系数异常小：$h_{thr}=(2/ \pi) \gamma + 0.002 \gamma^3$。 我们的方法基于在拐点附近孤子的奇异摄动展开；它允许以$h_{thr}(\gamma)$对$\gamma$的所有阶进行求解，并且可以很容易地重新表述为其他受扰孤子方程。 显示英文摘要

摘要： It has been known for some time that solitons of the externally driven, damped nonlinear Schr\"odinger equation can only exist if the driver's strength, $h$, exceeds approximately $(2/ \pi) \gamma$, where $\gamma$ is the dissipation coefficient. Although this perturbative result was expected to be correct only to the leading order in $\gamma$, recent studies have demonstrated that the formula $h_{thr}= (2 /\pi) \gamma$ gives a remarkably accurate description of the soliton's existence threshold prompting suggestions that it is, in fact, exact. In this note we evaluate the next order in the expansion of $h_{thr}(\gamma)$ showing that the actual reason for this phenomenon is simply that the next-order coefficient is anomalously small: $h_{thr}=(2/ \pi) \gamma + 0.002 \gamma^3$. Our approach is based on a singular perturbation expansion of the soliton near the turning point; it allows to evaluate $h_{thr}(\gamma)$ to all orders in $\gamma$ and can be easily reformulated for other perturbed soliton equations.