AB系统在椭圆函数背景下的多呼吸子  

Multiple Breathers of AB System Under Background of Elliptic Functions

作　　者：熊玮玥 张海强 姚慧 Xiong Weiyue;Zhang Haiqiang;Yao Hui(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《光学学报》2024年第5期161-169,共9页Acta Optica Sinica

基　　金：上海市自然科学基金(18ZR1426600)。

摘　　要：呼吸子泛指一类具有周期演化或周期分布结构的非线性波,它已成为非线性光学系统的研究热点之一。研究多种呼吸子的时空动力学特征具有实际的物理意义。本文基于孤子理论中的Darboux变换方法构造出AB系统在椭圆函数背景下的多呼吸子解,并进一步分析了呼吸子的非线性动力学特征。首先,基于AB系统的Lax对,通过修正的平方波函数法与行波变换法获得该系统的椭圆函数周期解以及Lax对的基本解。然后,通过椭圆函数积分公式和Darboux变换迭代算法,推导出dn和cn两种椭圆函数背景下的一阶和二阶呼吸子解的解析表达式。另外,讨论了三种呼吸子的动力学特征,主要包括一般呼吸子(GB)、Kuznetsov-Ma呼吸子(KMB)和Akhmediev呼吸子(AB)。最后,研究了在dn背景下GB和KMB相互作用的时空结构以及在cn背景下两个GB相互作用的时空结构。本文研究结果将有助于理解在非线性光学领域中周期背景下的呼吸子动力学特征和相互作用行为。Objective For current nonlinear physical systems,nonlinear optical fibers serve as a mature nonlinear experimental platform in experimental science.As a type of nonlinear wave with periodic evolution or periodic distribution structure,breathers have become one of the research hotspots in nonlinear optical systems.As the demand for long-distance and highcapacity fiber optic communication increases,the dynamic properties of breathers are receiving increasing attention.Studying the breather solutions for the AB system is of great significance for better understanding long-distance transmission without shape changing in fiber optic communication.In the context of the periodic solution of the AB system,we focus on the breathers of the system.By studying the interactions between two breathers,it is found that the collision between breathers is elastic,which means that breathers can be transported over long distances without changing their shapes.The results obtained in this article will help to understand the dynamics and interactions of breathers under periodic backgrounds in nonlinear optics.Methods Via the Darboux transformation method in soliton theory,multi-breather solutions for the AB system were constructed under the elliptic function background.With the help of Matlab software,the spatiotemporal structure of the breathers was plotted,and the nonlinear dynamic characteristics of these breathers were further analyzed.Firstly,elliptic function solutions of the AB system were solved by the modified squared wave(MSW)function approach and the traveling wave transformation.Then,we obtained the basic solution to the Lax pair corresponding to the seed solution to the Jacobi elliptic function.Based on the elliptic function transformation formulas and the integral formulas,the potential function solution could be expressed in terms of the Weierstrass elliptic function.Secondly,by the once-iterated Darboux transformation,three types of breather solutions under the elliptic function background were constructed including th

关 键 词：非线性光学 呼吸子 DARBOUX变换 AB系统 

分 类 号：O437[机械工程—光学工程]