Soliton solutions of the fifth order Caudrey-Dodd-Gibbon equation via a linear and nonlinear separate convolutional neural network

With the fast progress of information technology, machine learning is getting increasing attention. Among them, there are a growing body of researches on learning partial differential equations (PDEs) via Convolutional Neural Networks (CNNs). The linear and nonlinear separate network (LNSN) is a useful network for learning PDEs, and the Caudrey-Dodd-Gibbon (CDG) equation is an important PDE. As far as we know, the research on learning CDG equation via LNSN has never been documented. Therefore, we learn the CDG equation via the LNSN. In this work, we use the LNSN to learn one-soliton solution of the CDG equation. We compare results of one-soliton solution for the CDG equation via the LNSN under different time step sizes, training epochs, number of neurons per layer, and activation functions. It is found that the relative mean error (RME) can reach $\mathcal{O}\left( {{{10}^{ - 6}}} \right)$. Our experiments show the applicability of the LNSN for learning one-soliton solution of the CDG equation.