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

Jun Li(李军),Yong Chen(陈勇)

Figure 1. The KdV equation. Top: a one-soliton solution to the KdV equation (left panel) is compared to the corresponding predicted solution to the learned equation (right panel). The network correctly captures the dynamics behavior and accurately reproduces the soliton solution with a relative ${{\mathbb{L}}}_{2}$ error of 3.44 × 10–3 . Bottom: the comparison of the predicted and exact soliton solutions which correspond to the three temporal snapshots depicted by the white vertical lines in the top panel is presented.