Data-driven solutions and parameter discovery of the Sasa–Satsuma equation via the physics-informed neural networks method

Physics-informed neural networks (PINNs) can be used to predict various solutions of nonlinear partial differential equations in diverse physical fields. We use the PINNs to predict the (single-) double-hump soliton, multi-hump breather, anti-dark soliton, Mexican-hat soliton, twisted rogue-wave pairs and rational W-shaped soliton of the Sasa–Satsuma equation in optical fibers and deep water wave. The L2 relative error of the prediction results can achieve high accuracy even with only less training data and training time while the results show that the prediction error will increase with the increase of prediction time. In addition, we employ the PINNs to investigate the parameter discovery of the Sasa–Satsuma equation via the Mexican-hat soliton solution. For the anti-dark soliton, we compare the predicted results and the amount of data for the PINNs method and the traditional split-step Fourier technique, and show that the PINNs method requires less data with the same accuracy of prediction results.