A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
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DOI：
10.1002/cpa.21819
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发表时间：
2017-10
影响因子：
3
通讯作者：
Deniz Bilman;P. Miller
中科院分区：
文献类型：
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作者：
Deniz Bilman;P. Miller
我们对聚焦的非线性薛定谔方程(也是自然推广的其他方程)提出了一种修正的标准逆散射变换，该方程具有无穷远的非零边界条件。其目的是以一种简单和统一的方式处理任意阶极点和可能严重的谱奇异性。作为应用，我们首次使用改进的变换将Peregine解和相关的高阶“流氓波”解置于逆散射环境中。这使得人们可以直接研究这些解的性质，例如它们的动力学或结构稳定性，或者它们在高阶极限下的渐近行为。改进的变换方法还允许在其他结构上通过初等达布变换而不是文献中的广义达布变换或其他相关的极限过程来产生无赖波。©2019威利期刊公司。
We propose a modification of the standard inverse scattering transform for the focusing nonlinear Schrödinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity. The purpose is to deal with arbitrary‐order poles and potentially severe spectral singularities in a simple and unified way. As an application, we use the modified transform to place the Peregrine solution and related higher‐order “rogue wave” solutions in an inverse‐scattering context for the first time. This allows one to directly study properties of these solutions such as their dynamical or structural stability, or their asymptotic behavior in the limit of high order. The modified transform method also allows rogue waves to be generated on top of other structures by elementary Darboux transformations rather than the generalized Darboux transformations in the literature or other related limit processes. © 2019 Wiley Periodicals, Inc.