Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons, breathers, and rogue waves
Zijian Zhou, Zhenya Yan
Abstract
Abstract The dimensionless third-order nonlinear Schrödinger equation (alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g. bright soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated (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 bright solitons.
Topics & Concepts
BreatherRogue waveNonlinear Schrödinger equationPhysicsArtificial neural networkSolitonNonlinear systemNoise (video)Deep learningDeep waterStatistical physicsComputer scienceQuantum mechanicsArtificial intelligenceEngineeringImage (mathematics)Marine engineeringAdvanced Fiber Laser TechnologiesNonlinear Waves and SolitonsModel Reduction and Neural Networks