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

Jun Li(李军),Yong Chen(陈勇)

Figure 5. The KdV equation. Top: another two-soliton solution to the KdV equation (left panel) is compared to the predicted solution to the learned equation. The model correctly exhibits the dynamics behavior and accurately reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 2.53 × 10−2 . Bottom: the comparison of the predicted solutions and exact solutions is presented. The model training took about 7.5 min.