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

作　　者：Zijian Zhou Zhenya Yan 

机构地区：[1]Key Laboratory of Mathematics Mechanization,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Communications in Theoretical Physics》2021年第10期55-63,共9页理论物理通讯（英文版）

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

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.

关 键 词：third-order nonlinear Schrodinger equation deep learning data-driven solitons data-driven parameter discovery 

分 类 号：O175.29[理学—数学] TP18[理学—基础数学]