Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (7): 075007. doi: 10.1088/1572-9494/ac7202

• Mathematical Physics • Previous Articles     Next Articles

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

Shikun Cui1, Zhen Wang1,2,3,(), Jiaqi Han1, Xinyu Cui1, Qicheng Meng2   

  1. 1School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
    2State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou 310000, China
    3Key Laboratory for Computational Mathematics and Data Intelligence of Liaoning Province, Dalian 116024, China
  • Received: 2022-01-26 Revised: 2022-05-22 Accepted: 2022-05-23 Published: 2022-07-01
  • Contact: Zhen Wang E-mail:wangzhen@dlut.edu.cn

Abstract:

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 higher-order 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.

Key words: deep learning method, physics-informed neural networks, high-order nonlinear soliton equations, interaction between solitons, the numerical driven solution