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

Jun Li(李军),Yong Chen(陈勇)

Figure 3. The KdV equation. Top: a two-soliton solution to the KdV equation is compared to the corresponding predicted solution to the learned equation (right panel). The model correctly exhibits the dynamics behavior and accurately reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 7.39 × 10−2 . Bottom: the comparison of the predicted solutions and exact solutions which correspond to the three temporal snapshots is presented.