论文标题
圆球作为kuznetsov-ma和akhmedieev呼吸的局限性行为
Peregrine soliton as a limiting behavior of the Kuznetsov-Ma and Akhmediev breathers
论文作者
论文摘要
本文讨论了聚焦非线性Schrödinger（NLS）方程的呼吸溶液的限制行为。这些呼吸器属于孤子家族，在不变和恒定的背景下，连续的波信封是基座。理性的圆锥体是其他两个呼吸孤子的限制行为，即kuznetsov-ma的呼吸器和阿赫米德·索利顿。尽管有相移，但后者变成了在模量不稳定性现象中对应于不稳定模式的同型轨道波形的非线性扩展。所有呼吸都是非线性和分散媒体中流氓波的原型。我们使用$ε$ - $δ$参数提供了严格的证明，并显示了此限制行为的相应可视化。
This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger (NLS) equation. These breathers belong to the families of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic orbit waveform corresponding to an unstable mode in the modulational instability phenomenon. All breathers are prototypes for rogue waves in nonlinear and dispersive media. We present a rigorous proof using the $ε$-$δ$ argument and show the corresponding visualization for this limiting behavior.
