空间位移PT对称非局域非线性薛定谔方程的高阶怪波解  

General higher-order rogue waves in the space-shifted PT-symmetric nonlocal nonlinear Schrödinger equation

作　　者：饶继光 陈生安 吴昭君 贺劲松 Rao Ji-Guang;Chen Sheng-An;Wu Zhao-Jun;He Jin-Song(School of Mathematics and Statistics,Hubei University of Science and Technology,Xianning 437000,China;Institute for Advanced Study,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]湖北科技学院数学与统计学院,咸宁437000 [2]深圳大学高等研究院,深圳518060

出　　处：《物理学报》2023年第10期214-222,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12071304,12201195);湖北省自然科学基金(批准号:2022CFB818);湖北科技学院博士启动基金(批准号:BK202302);湖北科技学院科研创新团队资助项目(批准号:2022T05)资助的课题。

摘　　要：利用Kadomtsev-Petviashvili(KP)系列约束方法和双线性方法,构造了空间位移宇称-时间反演(PT)对称非局域非线性薛定谔方程的高阶怪波解.任意N阶怪波解的解析表达式是通过舒尔多项式表示的.首先通过分析一阶怪波解的动力学行为,发现怪波的最大振幅可以大于背景平面三倍的任意高度.分析了对称非局域非线性薛定谔方程中的空间位移因子x0在一阶怪波解中的影响,结果表明其仅改变怪波中心的位置.另外,研究了二阶怪波解的动力学行为以及怪波模式,然后给出了N阶怪波模式与N阶怪波解的解析表达式中参数之间的关系,进一步展示了高阶怪波的不同模式.General higher-order rogue wave solutions to the space-shifted PT-symmetric nonlocal nonlinear Schrödinger equation are constructed by employing the Kadomtsev-Petviashvili hierarchy reduction method.The analytical expressions for rogue wave solutions of any Nth-order are given through Schur polynomials.We first analyze the dynamics of the first-order rogue waves,and find that the maximum amplitude of the rogue waves can reach any height larger than three times of the constant background amplitude.The effects of the space-shifted factor x0 of the PT-symmetric nonlocal nonlinear Schrödinger equation in the first-order rogue wave solutions are studied,which only changes the center positions of the rogue waves.The dynamical behaviours and patterns of the second-order rogue waves are also analytically investigated.Then the relationships between Nth-order rogue wave patterns and the parameters in the analytical expressions of the rogue wave solutions are given,and the several different patterns of the higher-order rogue waves are further shown.

关 键 词：怪波 空间位移PT对称非局域非线性薛定谔方程 Kadomtsev-Petviashvili系列约束方法 

分 类 号：O175.29[理学—数学]