A deep learning method for solving third-order nonlinear evolution equations  

作　　者：Jun Li Yong Chen 李军;陈勇(Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai,200062,China;School of Mathematical Sciences,Shanghai Key Laboratory of PMMP,Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai,200062,China;College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,266590,China;Department of Physics,Zhejiang Normal University,Jinhua,321004,China)

机构地区：[1]Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai,200062,China [2]School of Mathematical Sciences,Shanghai Key Laboratory of PMMP,Shanghai Key Laboratory of Trustworthy Computing,East China Normal University,Shanghai,200062,China [3]College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,266590,China [4]Department of Physics,Zhejiang Normal University,Jinhua,321004,China

出　　处：《Communications in Theoretical Physics》2020年第11期19-29,共11页理论物理通讯（英文版）

基　　金：the support of the National Natural Science Foundation of China(No.11675054);the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213);the Science and Technology Commission of Shanghai Municipality(No.18dz2271000)。

摘　　要：It has still been difficult to solve nonlinear evolution equations analytically.In this paper,we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly.Specifically,the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters.In particular,numerical experiments on several third-order nonlinear evolution equations,including the Korteweg-de Vries(KdV)equation,modified KdV equation,KdV-Burgers equation and Sharma-Tasso-Olver equation,demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.

关 键 词：deep learning nonlinear evolution equations soliton interaction nonlinear dynamics 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O241.7[自动化与计算机技术—控制科学与工程]