Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with PT-symmetric harmonic potential via deep learning

Solving differential equations using deep neural networks

(2020) Craig Michoski et al.   NEUROCOMPUTING

Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

(2019) Christian Beck et al.   JOURNAL OF NONLINEAR SCIENCE

Multiple solutions for logarithmic Schrödinger equations

(2019) Wei Shuai   NONLINEARITY

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stable flat-top solitons and peakons in the P T-symmetric δ-signum potentials and nonlinear media

(2019) Yong Chen et al.   CHAOS

Multi-dimensional stable fundamental solitons and excitations in PT -symmetric harmonic-Gaussian potentials with unbounded gain-and-loss distributions

(2018) Yong Chen et al.   Communications in Nonlinear Science and Numerical Simulation

Universal dynamics for the defocusing logarithmic Schrödinger equation

(2018) Rémi Carles et al.   DUKE MATHEMATICAL JOURNAL

Optical solitons in periodically managed PT-symmetric media

(2018) F.Kh. Abdullaev et al.   OPTIK

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine learning of linear differential equations using Gaussian processes

(2017) Maziar Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stability of standing waves for NLS-log equation with $$\varvec{\delta }$$ δ -interaction

(2017) Jaime Angulo Pava et al.   NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses

(2017) Yong Chen et al.   Scientific Reports

On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT- and non- PT-symmetric potentials

(2016) Zhenya Yan et al.   CHAOS

Nonlinear switching and solitons in PT-symmetric photonic systems

(2016) Sergey V. Suchkov et al.   Laser & Photonics Reviews

Nonlinear waves inPT-symmetric systems

(2016) Vladimir V. Konotop et al.   REVIEWS OF MODERN PHYSICS

Deep learning

(2015) Yann LeCun et al.   NATURE

Solitons in a nonlinear Schrödinger equation withPT-symmetric potentials and inhomogeneous nonlinearity: Stability and excitation of nonlinear modes

(2015) Zhenya Yan et al.   PHYSICAL REVIEW A

Staggered parity-time-symmetric ladders with cubic nonlinearity

(2015) Jennie D'Ambroise et al.   PHYSICAL REVIEW E

Modulation of localized solutions for the Schrödinger equation with logarithm nonlinearity

(2014) L. Calaça et al.   Communications in Nonlinear Science and Numerical Simulation

Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials

(2014) Jianke Yang   OPTICS LETTERS

Complex PT-symmetric nonlinear Schrodinger equation and Burgers equation

(2013) Z. Yan   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Parity–time synthetic photonic lattices

(2012) Alois Regensburger et al.   NATURE

Stability analysis for solitons inPT-symmetric optical lattices

(2012) Sean Nixon et al.   PHYSICAL REVIEW A

Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences

(2010) K. G. Zloshchastiev   Gravitation & Cosmology

Observation of parity–time symmetry in optics

(2010) Christian E. Rüter et al.   Nature Physics

Observation ofPT-Symmetry Breaking in Complex Optical Potentials

(2009) A. Guo et al.   PHYSICAL REVIEW LETTERS

Optical Solitons inPTPeriodic Potentials

(2008) Z. H. Musslimani et al.   PHYSICAL REVIEW LETTERS