非局域反时空高阶非线性薛定谔方程的达布变换及其精确解

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 767-775.

非局域反时空高阶非线性薛定谔方程的达布变换及其精确解

鹿高杰¹,韩众¹,刘露^2,^*()

¹浙江金融职业学院信息技术学院杭州 310000
²山东科技大学经济管理学院山东青岛 266590

收稿日期:2024-07-08 修回日期:2024-11-14 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *刘露, E-mial: Magic_Liu@sdust.edu.cn
基金资助:
国家自然科学基金(72272089);国家自然科学基金(71902105);泰山学者工程专项经费(tsqn202312191)

Darboux Transformation and Exact Solutions of the Nonlocal Reverse Space-Time Higher-Order Nonlinear Schrödinger Equation

Lu Gaojie¹,Han Zhong¹,Liu Lu^2,^*()

¹Institute of Information Technology, Zhejiang Financial College, Hangzhou 310000
²School of Economics and Management, Shandong University of Science and Technology, Shandong Qingdao 266590

Received:2024-07-08 Revised:2024-11-14 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(72272089);NSFC(71902105);Special Fund of Taishan Scholars Project(tsqn202312191)

摘要/Abstract

摘要：

该文研究了由 Ablowitz-Kaup-Newell-Segur 线性散射问题导出的非局部反时空高阶非线性薛定谔方程. Darboux 变换是以行列式的形式提供的. 通过应用达布变换, 得到了非局部反时空高阶非线性薛定谔方程的精确解, 包括孤子解、复子解和怪波解. 最后, 解的动力学行为通过图解进行讨论. 这些结果可用于理解非线性光学和相关领域中的相关物理现象.

关键词: 非局域反时空高阶非线性薛定谔方程, 达布变换, 孤子, 复子解, 怪波

Abstract:

Under investigation in this paper is the nonlocal reverse space-time higher-order nonlinear Schrödinger (HNLS) equation which can be derived from the Ablowitz-Kaup-Newell-Segur linear scattering problem. The Darboux transformation is provided in the form of determinants. By applying the Darboux transformation, we arrive at exact solutions of the nonlocal reverse space-time HNLS equation, including soliton, complextion and rogue wave solutions. Finally, the dynamical behaviors of solutions are elucidated graphically. These results could be used to understand related physical phenomena in nonlinear optics and relevant fields.

Key words: the nonlocal reverse space-time higher-order nonlinear Schröodinger equation, Darboux transformation, soliton, complexiton solution, Rogue wave

中图分类号:

O175.24

鹿高杰, 韩众, 刘露. 非局域反时空高阶非线性薛定谔方程的达布变换及其精确解[J]. 数学物理学报, 2025, 45(3): 767-775.

Lu Gaojie, Han Zhong, Liu Lu. Darboux Transformation and Exact Solutions of the Nonlocal Reverse Space-Time Higher-Order Nonlinear Schrödinger Equation[J]. Acta mathematica scientia,Series A, 2025, 45(3): 767-775.

图/表 6

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图6

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