The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning

Abstract

We apply the deep learning approach to learn some nonlinear wave solutions of the Lakshmanan-Porsezian-Daniel (LPD) model characterizing the evolution of ultrashort optical pulse in optical fibers. Based on the strong universal approximation theorem, we give the initial-boundary value data and residual collocation points, choose the parameters initialization Xavier method and parameters optimization Adam and L-BFGS algorithms to construct the optimal neural network model. Then, we derive the data-driven solutions of the rogue wave, anti-dark soliton, multi-peak soliton, non-rational W-shaped soliton, rational W-shaped soliton as well as periodic-wave solutions for the LPD model. Finally, we study the parameters discovery of such model via the anti-dark soliton solution with 1% perturbation (or without perturbation).