A deep learning method for solving high-order nonlinear soliton equation
Pattern Formation and Solitons
2022-07-20 v1
Abstract
We propose effective scheme of deep learning method for high-order nonlinear soliton equation and compare the activation function for high-order soliton equation. The neural network approximates 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 equation, and verify its efficiency by solving the fourth-order Boussinesq equation and the fifth-order Korteweg de Vries equation. The results show that deep learning method can solve the high-order nonlinear soliton equation and reveal the interaction between solitons.
Keywords
Cite
@article{arxiv.2106.11024,
title = {A deep learning method for solving high-order nonlinear soliton equation},
author = {Shikun Cui and Zhen Wang and Jiaqi Han and Xinyu Cui},
journal= {arXiv preprint arXiv:2106.11024},
year = {2022}
}