推广的导数非线性薛定谔方程的单/双周期背景上的呼吸子和怪波及其碰撞解  

Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schrodinger Equation

作　　者：娄瑜 张翼[2] Lou Yu;Zhang Yi(Public Basic Education Department,Zhejiang Industry Polytechnic College,Zhejiang Shaoxing 312000;Department of Mathematics,Zhejiang Normal University,Zhejiang Jinhua 321004)

机构地区：[1]浙江工业职业技术学院公共基础教育部,浙江绍兴312000 [2]浙江师范大学数学科学学院,浙江金华321004

出　　处：《数学物理学报（A辑）》2024年第6期1511-1519,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11371326,11975145,12271488)

摘　　要：非线性薛定谔方程是物理和应用数学领域中一个非常重要的可积系统.该文利用达布变换研究了推广的导数非线性薛定谔方程的单/双周期背景上的呼吸子和怪波以及呼吸子和怪波的碰撞解.首先,构造推广的导数非线性薛定谔方程的达布变换.然后,通过达布变换,推导出周期背景和双周期背景上的呼吸子解和怪波解以及碰撞解.最后,借助于图示,详细分析了有趣的新解结构.这也为研究新型解的物理机制提供了理论依据.The nonlinear Schrodinger equation is a very important integrable system in the field of physics and applied mathematics.In this paper,the breather and rogue wave on the periodic/double periodic background and the collision solutions of breather and rogue wave for the generalized derivative nonlinear Schrodinger equation are studied by using the Darboux transformation.Firstly,the Darboux transformation of the generalized derivative nonlinear Schrodinger equation is constructed.Then,by using the Darboux transformation,the breather and rogue wave on the periodic/double periodic background and the collision solutions are derived.Finally,by means of the figures,the structures of interesting new solutions are analyzed in detail,which also provide a theoretical basis for studying the physical mechanism of the new solution.

关 键 词：推广的导数非线性薛定谔方程 达布变换 周期解 呼吸子 怪波 

分 类 号：O175.24[理学—数学]