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Inverse scattering method for the Kundu-Eckhaus equation with zero/nonzero boundary conditions
Zeitschrift für Naturforschung A ( IF 1.8 ) Pub Date : 2021-04-01 , DOI: 10.1515/zna-2020-0327
Guixian Wang 1 , Xiu-Bin Wang 1 , Bo Han 1 , Qi Xue 1
Affiliation  

In this paper, the inverse scattering approach is applied to the Kundu-Eckhaus equation with two cases of zero boundary condition (ZBC) and nonzero boundary conditions (NZBCs) at infinity. Firstly, we obtain the exact formulae of soliton solutions of three cases of N simple poles, one higher-order pole and multiple higher-order poles via the associated Riemann-Hilbert problem (RHP). Moreover, given the initial data that allow for the presence of discrete spectrum, the higher-order rogue waves of the equation are presented. For the case of NZBCs, we can construct the infinite order rogue waves through developing a suitable RHP. Finally, by choosing different parameters, we aim to show some prominent characteristics of this solution and express them graphically in detail. Our results should be helpful to further explore and enrich the related nonlinear wave phenomena.

中文翻译:

边界条件为零/非零的Kundu-Eckhaus方程的逆散射方法

在本文中,逆散射方法被应用于具有无限边界的零边界条件(ZBC)和非零边界条件(NZBCs)的两种情况的Kundu-Eckhaus方程。首先,通过相关的黎曼-希尔伯特问题(RHP),获得了N个简单极点,一个高阶极点和多个高阶极点三种情况的孤子解的精确公式。此外,在给出允许存在离散频谱的初始数据的情况下,给出了方程的高阶流氓波。对于NZBC,我们可以通过开发合适的RHP来构造无序流浪。最后,通过选择不同的参数,我们旨在显示该解决方案的一些突出特征,并以图形方式详细表示它们。
更新日期:2021-04-02
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