论文标题
审查展览和相关呼吸器的稳定性
Review on the stability of the Peregrine and related breathers
论文作者
论文摘要
在本说明中，我们回顾了三个重要的非线性Schrödinger呼吸器的能量空间中的稳定性：Peregrine，Kuznetsov-Ma和Akhmediev。更确切地说，我们表明，根据稳定性的标准定义，这些呼吸器是不稳定的。描述了合适的Lyapunov功能及其基础光谱特性。作为这些功能的第一个变化的直接结果，我们还提出了这些NLS呼吸器所实现的相应非线性ODE。最终讨论了上述每种呼吸器的全球稳定性概念。还简要提到了一些开放问题。
In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show that these breathers are unstable according to a standard definition of stability. Suitable Lyapunov functionals are described, as well as their underlying spectral properties. As an immediate consequence of the first variation of these functionals, we also present the corresponding nonlinear ODEs fulfilled by these NLS breathers. The notion of global stability for each breather above mentioned is finally discussed. Some open questions are also briefly mentioned.
