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

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.