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Bright-dark rogue wave transition in coupled AB system via the physics-informed neural networks method

Shi-Lin Zhang, Min-Hua Wang and Yin-Chuan Zhao

Vol. 19 (2024), No. 1, 1–26
Abstract

Physics-informed neural networks (PINNs) can be used not only to predict the solutions of nonlinear partial differential equations, but also to discover the dynamic characteristics and phase transitions of rogue waves in nonlinear systems. Based on improved PINNs, we predict bright-dark one-soliton, two-soliton, two-soliton molecule and rogue wave solutions in a coupled AB system. We find that using only a small number of dynamic evolutionary rogue wave solutions as training data, we can find the phase transition boundary that can distinguish bright and dark rogue waves, and realize the mutual prediction between different rogue wave structures. The results show that the improved algorithm has high prediction accuracy, which provides a promising general technique for discovering and predicting new rogue structures in other parametric coupled systems.

Keywords
AB system, physics informed neural network, rogue wave, phase transition
Mathematical Subject Classification
Primary: 65Y15
Secondary: 65N21
Milestones
Received: 14 October 2023
Revised: 22 February 2024
Accepted: 26 April 2024
Published: 17 June 2024
Authors
Shi-Lin Zhang
School of Mathematics and Physics
North China Electric Power University
Beijing
China
Min-Hua Wang
Department of Mining Engineering
Shanxi Institute of Energy
Shanxi
China
Yin-Chuan Zhao
School of Mathematics and Physics
North China Electric Power University
Beijing
China