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N-fold binary Darboux transformation for the nth-order Ablowitz–Kaup–Newell–Segur system under a pseudo-symmetry hypothesis
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-10-18 , DOI: 10.1016/j.aml.2021.107719
Jing-Jing Su 1, 2 , Bo Ruan 1
Affiliation  

In this paper, we introduce a pseudo-symmetry hypothesis, under which the N-fold binary Darboux transformation for the nth-order (n=1,0,1,) Ablowitz–Kaup–Newell–Segur (AKNS) system is presented in a unified form. Through the N-fold (N=1,2,3,) binary Darboux transformation, several high-order analytical solutions of certain nonlinear evolution equations can be obtained based on simple seed solutions. Especially, we take the well-known AB system as an example to present the Nth-order solitons. Moreover, the obtained results would be helpful to the developments of some computation algorithms on solving the nonlinear evolution equations.



中文翻译:

伪对称假设下 n 阶 Ablowitz-Kaup-Newell-Segur 系统的 N 折二元 Darboux 变换

在本文中,我们引入了一个伪对称假设,在该假设下, N-fold 二元 Darboux 变换 n三阶(n=-1,0,1,) Ablowitz-Kaup-Newell-Segur (AKNS) 系统以统一的形式呈现。通过N-折叠 (N=1,2,3,) 二元达布变换,基于简单的种子解可以得到某些非线性演化方程的几个高阶解析解。特别是,我们以著名的AB系统为例来介绍N三阶孤子。此外,所获得的结果将有助于一些求解非线性演化方程的计算算法的发展。

更新日期:2021-10-28
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