A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation

DOI10.1016/j.cnsns.2021.105896zbMath1480.35363OpenAlexW3164864419MaRDI QIDQ2038155

Ruiqi Wang, Delu Zeng, Bao-Feng Feng, Liming Ling

Publication date: 9 July 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2021.105896

zbMATH Keywords

nonlinear Schrödinger equationnumerical simulationrogue wavebreatherdeep learning

Mathematics Subject Classification ID

Computational learning theory (68Q32) Artificial neural networks and deep learning (68T07) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Solitary waves for incompressible inviscid fluids (76B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (5)

\(N\)-double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm ⋮ The Fermi-Pasta-Ulam-Tsingou recurrence for discrete systems: cascading mechanism and machine learning for the Ablowitz-Ladik equation ⋮ A homotopy gated recurrent unit for predicting high dimensional hyperchaos ⋮ Dynamic analysis on optical pulses via modified PINNs: soliton solutions, rogue waves and parameter discovery of the CQ-NLSE ⋮ Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

Uses Software

• Adam
• DGM

Cites Work

• Unnamed Item
• Unnamed Item
• Akhmediev breather evolution in optical fiber for realistic initial conditions
• Pseudo-spectral solution of nonlinear Schrödinger equations
• Extreme waves that appear from nowhere: on the nature of rogue waves
• Rogue wave triplets
• Split-step spectral method for nonlinear Schrödinger equation with abosorbing boundaries
• On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
• Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• Generalized Galerkin approximations of elastic waves with absorbing boundary conditions
• DGM: a deep learning algorithm for solving partial differential equations
• Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrödinger equation
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Observation of rogue wave triplets in water waves
• Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation
• Water waves, nonlinear Schrödinger equations and their solutions
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Finite difference discretization of the cubic Schrödinger equation
• Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability
• A PseudoSpectral Procedure for the Solution of Nonlinear Wave Equations with Examples from Free-Surface Flows
• Solving Fokker-Planck equation using deep learning
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
• The disintegration of wave trains on deep water Part 1. Theory
• On the Construction and Comparison of Difference Schemes
• Accurate solution of the Orr–Sommerfeld stability equation
• Multi-symplectic Fourier pseudospectral method for the nonlinear Schrödinger equation
• Solving second-order nonlinear evolution partial differential equations using deep learning
• A deep learning method for solving third-order nonlinear evolution equations

This page was built for publication: A deep learning improved numerical method for the simulation of rogue waves of nonlinear Schrödinger equation