Deep learning soliton dynamics and complex potentials recognition for 1D and 2D \(\mathcal{PT}\)-symmetric saturable nonlinear Schrödinger equations

DOI10.1016/j.physd.2023.133729MaRDI QIDQ6160033

Zhenya Yan, Jin Song

Publication date: 8 May 2023

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

soliton dynamicsdeep neural network learning\(\mathcal{PT}\)-symmetric non-periodic and periodic potentials1D and 2D saturable nonlinear Schrödinger equationcomplex potentials recognition

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Pattern recognition, speech recognition (68T10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (3)

VC-PINN: variable coefficient physics-informed neural network for forward and inverse problems of PDEs with variable coefficient ⋮ Deep learning data-driven multi-soliton dynamics and parameters discovery for the fifth-order Kaup-Kuperschmidt equation ⋮ A new method for solving nonlinear partial differential equations based on liquid time-constant networks

Cites Work

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• Solving forward and inverse problems of the logarithmic nonlinear Schrödinger equation with \(\mathcal{PT}\)-symmetric harmonic potential via deep learning
• Newton-conjugate-gradient methods for solitary wave computations
• On the limited memory BFGS method for large scale optimization
• Vector financial rogue waves
• Data-driven peakon and periodic peakon solutions and parameter discovery of some nonlinear dispersive equations via deep learning
• A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
• \(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm
• Data-driven rogue waves and parameters discovery in nearly integrable \(\mathcal{PT}\)-symmetric Gross-Pitaevskii equations via PINNs deep learning
• Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
• Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Multidimensional dissipative solitons and solitary vortices
• Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions
• Spectral Methods in MATLAB
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• The nonlinear Schrödinger equation with generalized nonlinearities and PT-symmetric potentials: Stable solitons, interactions, and excitations
• Deformation of dark solitons in a PT-invariant variable coefficients nonlocal nonlinear Schrödinger equation
• DeepXDE: A Deep Learning Library for Solving Differential Equations
• fPINNs: Fractional Physics-Informed Neural Networks
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential
• A physics-constrained deep residual network for solving the sine-Gordon equation
• A deep learning method for solving third-order nonlinear evolution equations

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