148 citations · 324 across the 13 of their papers we have counts for
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nlin.PS2021★ 1 cited
Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
Zijian Zhou, Li Wang, Zhenya Yan
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 Schrödinger (spin-NLS) equation v…
cs.LG2021★ 29 cited
Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes
Zijian Zhou, Li Wang, Weifang Weng +1
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 solito…
nlin.PS2021★ 59 cited
Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learning
Li Wang, Zhenya Yan
In the field of mathematical physics, there exist many physically interesting nonlinear dispersive equations with peakon solutions, which are solitary waves with discontinuous firs…