PINN deep learning for the Chen-Lee-Liu equation: Rogue wave on the periodic background

TL;DR

This paper introduces a novel application of physics-informed neural networks (PINNs) to accurately model rogue waves and other solutions of the Chen-Lee-Liu equation, including the first data-driven rogue periodic wave.

Contribution

It presents the first data-driven approach using PINNs to solve the Chen-Lee-Liu equation and demonstrates its effectiveness in modeling various wave solutions.

Findings

PINNs accurately model rogue, breather, soliton, and periodic waves.

First data-driven rogue periodic wave solution for Chen-Lee-Liu equation.

Numerical results confirm the effectiveness of PINNs in wave solution generation.

Abstract

We consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen-Lee-Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method is applied to research the data-driven rogue periodic wave, breather wave, soliton wave and periodic wave solutions of well-known Chen-Lee-Liu equation. Especially, the data-driven rogue periodic wave is learned for the first time to solve the partial differential equation. In addition, using image simulation, the relevant dynamical behaviors and error analysis for there solutions are presented. The numerical results indicate that the rogue periodic wave, breather wave, soliton wave and periodic wave solutions for Chen-Lee-Liu equation can be generated well by PINNs deep learning method.