Deep learning neural networks for the third-order nonlinear Schrodinger equation: bright solitons, breathers, and rogue waves

作     者：Zijian Zhou Zhenya Yan Zijian Zhou;Zhenya Yan

作者机构：Key Laboratory of Mathematics MechanizationAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2021年第73卷第10期

页      面：55-63页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0704[理学-天文学] 0701[理学-数学] 0811[工学-控制科学与工程] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(Nos.11925108 and 11731014) 

主　　题：third-order nonlinear Schrodinger equation deep learning data-driven solitons data-driven parameter discovery 

摘      要：The dimensionless third-order nonlinear Schrodinger equation(alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks(PINNs) deep learning method to explore the data-driven solutions(e.g. bright soliton,breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated(a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.