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

TL;DR

This paper introduces an improved physics-informed neural network (IPINN) method with adaptive activation functions to accurately derive various localized wave solutions of the derivative nonlinear Schrödinger equation, including for the first time the periodic and rogue periodic waves.

Contribution

The paper presents a novel IPINN approach with neuron-wise adaptive activation functions for solving the DNLS and explores new wave solutions like periodic and rogue periodic waves.

Findings

IPINN accurately models localized wave solutions of DNLS.

First-time investigation of periodic and rogue periodic waves using IPINN.

Method performs well with small data sets.

Abstract

The research of the derivative nonlinear Schrodinger equation (DNLS) has attracted more and more extensive attention in theoretical analysis and physical application. The improved physicsinformed 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 data-driven periodic wave and rogue periodic wave of the DNLS are investigated by employing the IPINN method for the first time. Furthermore, the relevant dynamical behaviors, error analysis and vivid plots have been exhibited in detail. The numerical results indicate the IPINN method can well simulate the localized wave solutions of the DNLS under a small data set.