148 citations · 324 across the 13 of their papers we have counts for
13 papers
Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?
Zijian Zhou, Zhenya Yan
In this paper, we study the neural tangent kernel (NTK) for general partial differential equations (PDEs) based on physics-informed neural networks (PINNs). As we all know, the tra…
Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schrödinger equations
Jin Song, Zhenya Yan
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 Schröding…
Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones
Junchao Chen, Jin Song, Zijian Zhou +1
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 n…
Symmetry breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials
Jin Song, Boris A. Malomed, Zhenya Yan
We address symmetry breaking bifurcations (SBBs) in the ground-state (GS) and dipole-mode (DM) solitons of the 1D linearly coupled NLS equations, modeling the propagation of light…
Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential
Jin Song, Zhenya Yan, Boris A. Malomed
In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with L…
Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
Ming Zhong, Li Wang, Pengfei Li +1
We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger (FNLS) equation with focusing saturable…
Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy
Minghe Zhang, Weifang Weng, Zhenya Yan
In this paper, we investigate the anomalous dispersive relations, inverse scattering transform with a Riemann-Hilbert (RH) problem, and fractional multi-solitons of the integrable…
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…
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…
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…
Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learning
Li Wang, Zhenya Yan
The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the mu…
Rogue wave formation and interactions in the defocusing nonlinear Schrödinger equation with external potentials
Li Wang, Zhenya Yan
The defocusing nonlinear Schrödinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we fi…
Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
Li Wang, Boris A. Malomed, Zhenya Yan
We introduce a model based on the one-dimensional nonlinear Schroedinger equation (NLSE) with the critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate tha…