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

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.