Use of BNNM for interference wave solutions of the gBS-like equation and comparison with PINNs
This work addresses a specific mathematical physics problem for researchers in soliton theory and neural network applications, but it is incremental as it builds on existing methods like PINNs.
The authors tackled the problem of solving the generalized broken soliton-like equation by deriving it and using neural networks to find interference wave solutions, achieving zero error in fitting explicit solutions and showing that the bilinear neural network method is more accurate and faster than physical informed neural networks.
In this work, the generalized broken soliton-like (gBS-like) equation is derived through the generalized bilinear method. The neural network model, which can fit the explicit solution with zero error, is found. The interference wave solution of the gBS-like equation is obtained by using the bilinear neural network method (BNNM) and physical informed neural networks (PINNs). Interference waves are shown well via three-dimensional plots and density plots. Compared with PINNs, the bilinear neural network method is not only more accurate but also faster.