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Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones
In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm.
Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schrödinger equations
In this paper, we firstly extend the physics-informed neural networks (PINNs) to learn data-driven stationary and non-stationary solitons of 1D and 2D saturable nonlinear Schr\"odinger equations (SNLSEs) with two fundamental PT-symmetric Scarf-II and periodic potentials in optical fibers.
Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator
The results obtained in this paper may be useful to further understand the neural networks in the fractional integrable nonlinear wave systems and the mappings between two spaces.
Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning.
Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes
We introduce a deep neural network learning scheme to learn the B\"acklund transforms (BTs) of soliton evolution equations and an enhanced deep learning scheme for data-driven soliton equation discovery based on the known BTs, respectively.
Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wave in plasma and the wave propagation of ultrashort light pulses in optical fibers, as well as broader-banded waves on deep water.
Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning
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.
Higher-order vector Peregrine solitons and asymptotic estimates for the multi-component nonlinear Schrödinger equations
We first report the first- and higher-order vector Peregrine solitons (alias rational rogue waves) for the any multi-component NLS equations based on the loop group theory, an explicit (n + 1)-multiple eigenvalue of a characteristic polynomial of degree (n + 1) related to the condition of Benjamin-Feir instability, and inverse functions.
Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Mathematical Physics Pattern Formation and Solitons Computational Physics
Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
The extreme events are investigated for an $n$-component nonlinear Schr\"odinger ($n$-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields.
Exactly Solvable and Integrable Systems Mathematical Physics Analysis of PDEs Mathematical Physics Pattern Formation and Solitons Optics
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution.
