A deep learning method for solving high-order nonlinear soliton equations  

作　　者：Shikun Cui Zhen Wang Jiaqi Han Xinyu Cui Qicheng Meng 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,Ministry of Natural Resources,Hangzhou 310o00,China [3]Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province,Dalian 116024,Chin

出　　处：《Communications in Theoretical Physics》2022年第7期57-69,共13页理论物理通讯（英文版）

基　　金：supported by National Science Foundation of China(52171251);Liao Ning Revitalization Talents Program(XLYC1907014);the Fundamental Research Funds for the Central Universities(DUT21ZD205);Ministry of Industry and Information Technology(2019-357);the Project of State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography,MNR(QNHX2112)。

摘　　要：We propose an effective scheme of the deep learning method for high-order nonlinear soliton equations and explore the influence of activation functions on the calculation results for higherorder nonlinear soliton equations. The physics-informed neural networks approximate the solution of the equation under the conditions of differential operator, initial condition and boundary condition. We apply this method to high-order nonlinear soliton equations, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg–de Vries equation. The results show that the deep learning method can be used to solve high-order nonlinear soliton equations and reveal the interaction between solitons.

关 键 词：deep learning method physics-informed neural networks high-order nonlinear soliton equations interaction between solitons the numerical driven solution 

分 类 号：O175[理学—数学] TP18[理学—基础数学]