Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning
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Abstract (arXiv)
In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves with discontinuous first-order derivative at the wave peak. In this paper, we apply the multi-layer physics-informed neural networks (PINNs) deep learning to successfully study the data-driven peakon and periodic peakon solutions of some well-known nonlinear dispersion equations with initial-boundary value conditions such as the Camassa-Holm (CH) equation, Degasperis-Procesi equation, modified CH equation with cubic nonlinearity, Novikov equation with cubic nonlinearity, mCH-Novikov equation, b-family equation with quartic nonlinearity, generalized modified CH equation with quintic nonlinearity, and etc. These results will be useful to further study the peakon solutions and corresponding experimental design of nonlinear dispersive equations.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 9 of its 51 references that are in the map. First posted on arXiv 12 Jan 2021.
Builds on
9 of 51 references.
References · 9
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- 2019Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networkscited by 63
- 2020Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flowscited by 36
- 2020Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learningcited by 12
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Citing papers per year: 2021: 2; 2022: 0; 2023: 2; 2024: 2.
6 papers.
- 2024Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?cited by 5
- 2023Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schr"odinger equationscited by 3
- 2024Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equationscited by 2
- 2021Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemescited by 1
- 2021Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitonscited by 0
- 2023Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zonescited by 0
- 2024Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?9 Dec 2024
- 2024Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations2 Sep 2024
- 2023Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schr"odinger equations29 Sep 2023
- 2023Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones29 Sep 2023
- 2021Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons28 Dec 2021
- 2021Data-driven discoveries of B"acklund transforms and soliton evolution equations via deep neural network learning schemes18 Nov 2021