对跃迁耦合非线性薛定谔方程的平面波/周期背景上的怪波与呼吸波的相互作用解

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1742-1750.

对跃迁耦合非线性薛定谔方程的平面波/周期背景上的怪波与呼吸波的相互作用解

鹿高杰¹(), 张雯韵²(), 张翼³^,^*(), 娄瑜⁴()

¹ 浙江金融职业学院信息技术学院杭州 310000
² 嘉兴职业技术学院现代商贸学院浙江嘉兴 314036
³ 浙江师范大学数学科学学院浙江金华 321004
⁴ 浙江工业职业技术学院公共基础教学部浙江绍兴 312000

收稿日期:2025-06-10 修回日期:2025-10-21 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 张翼 E-mail:boyangbeyond@outlook.com;718780462@qq.com;zy2836@163.com;lyzjipc@163.com
作者简介:鹿高杰, E-mail:boyangbeyond@outlook.com;
张雯韵, E-mail:718780462@qq.com;
娄瑜, E-mail:lyzjipc@163.com
基金资助:
国家自然科学基金(11371326);国家自然科学基金(12271488);浙江省省属高校基本科研业务费(2025ZD26)

Interactions of Rogue Waves and Breathers On the Plane Wave/Periodic Background for the Pair-Transition-Coupled Nonlinear Schrödinger Equations

Gaojie Lu¹(), Wenyun Zhang²(), Yi Zhang³^,^*(), Yu Lou⁴()

¹ College of Information Technology, Zhejiang Financial College, Hangzhou 310000
² College of Modern Commerce, Jiaxing Vocational Institute, Zhejiang Jiaxing 314036
³ Department of Mathematics, Zhejiang Normal University, Zhejiang Jinhua 321004
⁴ Public Basic Education Department, Zhejiang Industry Polytechnic College, Zhejiang Shaoxing 312000

Received:2025-06-10 Revised:2025-10-21 Online:2026-10-26 Published:2026-09-07
Contact: Yi Zhang E-mail:boyangbeyond@outlook.com;718780462@qq.com;zy2836@163.com;lyzjipc@163.com
Supported by:
NSFC(11371326);NSFC(12271488);Fundamental Research Fundsfor the Provincial Universities of Zhejiang(2025ZD26)

摘要/Abstract

摘要：

该文探究了描述正交偏振光波传播的对跃迁耦合非线性薛定谔方程. 根据其 Lax 对, 可以构造 $N$ 重广义达布变换. 通过选择不同的种子解, 作者得到了平面波/周期背景上各种类型的新型怪波和呼吸波的相互作用解. 特别指出的是, 得到了与普通的怪波和呼吸波不同的新的怪波和呼吸波. 此外, 通过图像具体展示了参数变化对解的位置、角度、结构和能量分布的影响, 并讨论了它们的相互作用性质. 这些结果能为其他可积系统在不同背景上的局域波研究带来启示.

关键词: 对跃迁耦合非线性薛定谔方程, 广义达布变换, 怪波, 呼吸波, 周期背景

Abstract:

In this paper, we explore the pair-transition-coupled nonlinear Schrödinger equations, which can describe the propagation of orthogonally polarized optical waves. According to the Lax pair, the $N$-fold generalized Darboux transformation can be constructed. As applications, choosing distinct seed solutions, we obtain interactions of diverse types of novel rogue waves and breathers on the plane wave/periodic background. Especially, it is observed that some of rogue waves and breathers with special wave shapes are extremely different from other common rogue waves and breathers. Moreover, the position, angle, structure and energy distribution of these solutions influenced by parameters are exhibited graphically and we discuss their interaction properties. These results will shed light on the study of localized waves on the various backgrounds for other integrable systems.

Key words: pair-transition-coupled nonlinear Schrödinger equations, generalized Darboux transformation, rogue waves, breathers, periodic background

中图分类号:

O175.24

鹿高杰, 张雯韵, 张翼, 娄瑜. 对跃迁耦合非线性薛定谔方程的平面波/周期背景上的怪波与呼吸波的相互作用解[J]. 数学物理学报, 2026, 46(5): 1742-1750.

Gaojie Lu, Wenyun Zhang, Yi Zhang, Yu Lou. Interactions of Rogue Waves and Breathers On the Plane Wave/Periodic Background for the Pair-Transition-Coupled Nonlinear Schrödinger Equations[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1742-1750.

图/表 6

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