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孤子解、呼吸子解和有理波解的广义非线性薛定谔方程的达布变换。

Soliton solution, breather solution and rational wave solution for a generalized nonlinear Schrödinger equation with Darboux transformation.

机构信息

School of Mathematics and Systematic Sciences, Shenyang Normal University, Shenyang, 110034, China.

出版信息

Sci Rep. 2023 Jun 9;13(1):9406. doi: 10.1038/s41598-023-36295-x.

DOI:10.1038/s41598-023-36295-x
PMID:37296203
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10256863/
Abstract

In this paper, the exact solutions of generalized nonlinear Schrödinger (GNLS) equation are obtained by using Darboux transformation(DT). We derive some expressions of the 1-solitons, 2-solitons and n-soliton solutions of the GNLS equation via constructing special Lax pairs. And we choose different seed solutions and solve the GNLS equation to obtain the soliton solutions, breather solutions and rational wave solutions. Based on these obtained solutions, we consider the elastic interactions and dynamics between two solitons.

摘要

本文利用达布变换（DT）获得了广义非线性薛定谔（GNLS）方程的精确解。我们通过构造特殊的Lax 对，推导出了 GNLS 方程的 1-孤子、2-孤子和 n-孤子解的一些表达式。并且我们选择了不同的种子解来求解 GNLS 方程，得到了孤子解、呼吸子解和有理波解。基于这些得到的解，我们考虑了两个孤子之间的弹性相互作用和动力学。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/94004c7bfb3c/41598_2023_36295_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/d2dc6fa41c09/41598_2023_36295_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/8299e19c71d1/41598_2023_36295_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/bc6ea45cdefd/41598_2023_36295_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/e64ac60e45dc/41598_2023_36295_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/94004c7bfb3c/41598_2023_36295_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/d2dc6fa41c09/41598_2023_36295_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/8299e19c71d1/41598_2023_36295_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/bc6ea45cdefd/41598_2023_36295_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/e64ac60e45dc/41598_2023_36295_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6295/10256863/94004c7bfb3c/41598_2023_36295_Fig5_HTML.jpg

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本文引用的文献

1
Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.具有PT对称势的Ablowitz-Musslimani方程的非自治离散 rogue 波解的动力学
Chaos. 2017 Feb;27(2):023108. doi: 10.1063/1.4975763.
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Integrable nonlocal nonlinear Schrödinger equation.可积非局域非线性薛定谔方程。
Phys Rev Lett. 2013 Feb 8;110(6):064105. doi: 10.1103/PhysRevLett.110.064105. Epub 2013 Feb 7.
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Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.非线性薛定谔方程：广义达布变换与 rogue 波解。
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 2):026607. doi: 10.1103/PhysRevE.85.026607. Epub 2012 Feb 27.