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

• Published in: Communications in nonlinear science & numerical simulation Vol. 105; p. 106067
• Main Authors: Peng, Wei-Qi, Pu, Jun-Cai, Chen, Yong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.02.2022; Elsevier Science Ltd
• Subjects: Breather wave; Deep learning; Error analysis; Multilayers; Neural networks; Partial differential equations; Periodic wave; Physics-informed neural networks; Propagation; Rogue periodic wave; Schrodinger equation; Solitary waves; Soliton wave; Surface waves; The Chen–Lee–Liu equation; Deep learning; Rogue periodic wave; Soliton wave; Periodic wave; The Chen–Lee–Liu equation; Breather wave; Physics-informed neural networks
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2021.106067

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. •The rogue periodic wave and periodic wave for CLL equation are derived firstly.•The PINN method is applied to research the data-driven solutions of CLL equation.•The data-driven rogue periodic wave is learned for the first time to solve the PDE.