摘要
首先给出非自治Kadomtsev-Petviashvili方程转换为Kadomtsev-Petviashvili方程的一个自相似变换,然后基于Kadomtsev-Petviashvili方程的Lump解构造了非自治Kadomtsev-Petviashvili方程的有理函数表示的二维单、双、三怪波解,最后通过合适选取变参数,用图示说明了它们的演化特征,并利用快速傅里叶变换算法数值模拟测试了二维单怪波的动力学稳定性.本文方法对寻找(2+1)维非线性波动模型的怪波激发提供了启迪.
Rogue wave is a kind of natural phenomenon that is fascinating,rare,and extreme.It has become a frontier of academic research.The rogue wave is considered as a spatiotemporal local rational function solution of nonlinear wave model.There are still very few(2+1)-dimensional nonlinear wave models which have rogue wave solutions,in comparison with soliton and Lump waves that are found in almost all(2+1)-dimensional nonlinear wave models and can be solved by different methods,such as inverse scattering method,Hirota bilinear method,Darboux transform method,Riemann-Hilbert method,and homoclinic test method.The structure and evolution characteristics of the obtained(2+1)-dimensional rogue waves are quite different from the prototypes of the(1+1)-dimensional nonlinear Schrödinger equation.Therefore,it is of great value to study two-dimensional rogue waves.In this paper,the non-autonomous Kadomtsev-Petviashvili equation is first converted into the Kadomtsev-Petviashvili equation with the aid of a similar transformation,then two-dimensional rogue wave solutions represented by the rational functions of the non-autonomous Kadomtsev-Petviashvili equation are constructed based on the Lump solution of the first kind of Kadomtsev-Petviashvili equation,and their evolutionary characteristics are illustrated by images through appropriately selecting the variable parameters and the dynamic stability of two-dimensional single rogue waves is numerically simulated by the fast Fourier transform algorithm.The obtained two-dimensional rogue waves,which are localized in both space and time,can be viewed as a two-dimensional analogue to the Peregrine soliton and thus are a natural candidate for describing the rogue wave phenomena.The method presented here provides enlightenment for searching for rogue wave excitation of(2+1)-dimensional nonlinear wave models.We show that two-dimensional rogue waves are localized in both space and time which arise from the zero background and then disappear into the zero background again.These rogue-wave solutions to the nonautonomous Kadomtsev-Petviashvili equation generalize the rogue waves of the nonlinear Schrödinger equation into two spatial dimensions,and they could play a role in physically understanding the rogue water waves in the ocean.
作者
张解放
金美贞
胡文成
Zhang Jie-Fang;Jin Mei-Zhen;Hu Wen-Cheng(Institute of Intelligent Media Technology,Communication University of Zhejiang,Hangzhou 310018,China;Zhejiang Provincial Key Laboratory of Film and Television Media Technology,Communication University of Zhejiang,Hangzhou 310018,China;Network Data Center,Communication University of Zhejiang,Hangzhou 310018,China;College of Science,Zhongyuan University of Technology,Zhengzhou 450007,China)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2020年第24期163-174,共12页
Acta Physica Sinica
基金
国家自然科学基金(批准号:61877053)资助的课题.
作者简介
通信作者:张解放.E-mail:Zhangjief@cuz.edu.cn。
