Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves

The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes strongly dispersive ion-acoustic wave in plasma and propagation of ultrashort light pulses optical fibers, as well broader-banded waves on water. In this paper, we use physics-informed networks (PINNs) learning method to explore data-driven solutions (e.g., soliton, breather, rogue waves) when two types unperturbated (a 2% noise) training data are considered. Moreover, PINNs study discovery parameters appearing with aid solitons.