The data-driven localized wave solutions of the derivative nonlinear Schrödinger equation by using improved PINN approach

Abstract

The research of the derivative nonlinear Schrödinger equation (DNLS) has attracted more and more extensive attention in theoretical analysis and physical application. The improved physics-informed neural network (IPINN) approach with neuron-wise locally adaptive activation function is presented to derive the data-driven localized wave solutions, which contain rational solution, soliton solution, rogue wave, periodic wave and rogue periodic wave for the DNLS with initial and boundary conditions in complex space. Especially, the flow-process diagram that accounts for the IPINN of DNLS equation has been outline in detail, and the data-driven periodic wave and rogue periodic wave of the DNLS are investigated by employing the IPINN method for the first time. The numerical results indicate the IPINN method can well simulate the localized wave solutions of the DNLS. Furthermore, the relevant dynamical behaviors, error analysis and vivid plots have been exhibited in detail.