Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
This work provides a method for studying rogue wave solutions and parameter discovery in the NLS equation, which is relevant for researchers in nonlinear physics and deep learning applications to PDEs.
This paper investigates data-driven rogue wave solutions for the defocusing nonlinear Schrödinger (NLS) equation with a time-dependent potential using physics-informed neural networks (PINNs). It explores various initial conditions and also demonstrates the PINN algorithm's ability to discover parameters within the NLS equation.
The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schrödinger (NLS) equation with the time-dependent potential by considering several initial conditions such as the rogue wave, Jacobi elliptic cosine function, two-Gaussian function, or three-hyperbolic-secant function, and periodic boundary conditions. Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution. These results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.