Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
This work addresses wave modeling in physics domains such as plasma and optics, but it is incremental as it applies an existing PINN method to a specific equation.
The paper tackles the problem of solving the third-order nonlinear Schrödinger (Hirota) equation for complex wave phenomena like solitons, breathers, and rogue waves, using physics-informed neural networks (PINNs) to achieve data-driven solutions and parameter discovery, with results including handling 2% noise in training data.
The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wave in plasma and the wave propagation of ultrashort light pulses in optical fibers, as well as broader-banded waves on deep water. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g., soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and unperturbated (a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of solitons.