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Rogue wave formation and interactions in the defocusing nonlinear Schrödinger equation with external potentials
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2020-08-07 , DOI: 10.1016/j.aml.2020.106670
Li Wang , Zhenya Yan

The defocusing nonlinear Schrödinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in the defocusing NLS equation with real-valued time-dependent and time-independent potentials such that the stable new RWs and W-shaped solitons are found, respectively. Moreover, the interactions of two or three RWs are explored such that the RWs with higher amplitudes are generated in the defocusing NLS equation with real-valued time-dependent potentials. Finally, we study the defocusing NLS equation with complex PT-symmetric potentials such that some RWs and W-shaped solitons are also found. These novel results will be useful to design the related physical experiments to generate the RW phenomena and W-shaped solitons in the case of defocusing nonlinear interactions, and to apply them in the related fields of nonlinear or even linear sciences.



中文翻译:

散焦非线性Schrödinger方程中具有外部势的无赖波形成和相互作用

散焦非线性Schrödinger(NLS)方程没有调制不稳定性,并且至今尚未发现具有流浪(RW)现象。在本文中,我们首先研究了散焦NLS方程中的一些新颖的非线性波结构,它们具有与实值相关的时间和与时间无关的电势,从而分别找到了稳定的新RW和W形孤子。此外,探索了两个或三个RW的相互作用,以便在散焦NLS方程中生成具有更高幅度的RW,并具有与实值相关的时势。最后,我们研究了具有复数形式的散焦NLS方程PT对称电位,例如一些RW和W形孤子。这些新颖的结果将有助于设计相关的物理实验,以在散焦非线性相互作用的情况下生成RW现象和W形孤子,并将其应用于非线性甚至线性科学的相关领域。

更新日期:2020-08-07
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