Peakons of the shallow-water wave equation implementation with PINNs

Abstract In this paper, we implement the peakon solution of the CH equation containing highly nonlinear terms using the Physics-Informed Neural Networks, and we define the corresponding neural network models according to different forms of peakon solution expressions. The main implementation is to study the spatio-temporal dynamics behaviour of the peakon solution for the general form of the CH equations. From the experimental results, the Physics-Informed Neural Networks can basically complete the analytical solution prediction of the shallow-water wave equation, and achieve the accurate capture of highly complex nonlinear terms, which proves the successful application of the Physics-Informed Neural Networks method in the peakon solution of the shallow-water wave equation.