Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes
arXiv:2111.09489 · doi:10.1016/j.physleta.2022.128373
Abstract
We introduce a deep neural network learning scheme to learn the Bäcklund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively. The first scheme takes advantage of some solution (or soliton equation) information to study the data-driven BT of sine-Gordon equation, and complex and real Miura transforms between the defocusing (focusing) mKdV equation and KdV equation, as well as the data-driven mKdV equation discovery via the Miura transforms. The second deep learning scheme uses the explicit/implicit BTs generating the higher-order solitons to train the data-driven discovery of mKdV and sine-Gordon equations, in which the high-order solution informations are more powerful for the enhanced leaning soliton equations with higher accurates.
25 pages, 12 figures
References in corpus (9)
- Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
- A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
- Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
- Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach
- -double poles solutions for nonlocal Hirota equation with nonzero boundary conditions using Riemann-Hilbert method and PINN algorithm
- Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
- Physics-informed neural networks method in high-dimensional integrable systems
- Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning
- Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves