Zhenya Yan
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Bearing-Weak-Fault Signal Enhancement and Diagnosis Based on Multivariate Statistical Hilbert Differential TEO Open
The enhancement of weak-fault signal characteristics in rolling bearings under strong background noise interference has always been a challenging problem in rotating machinery fault diagnosis. Research indicates that multivariate statistic…
View article: Gap solitons and vortices in two-dimensional spin-orbit-coupled Bose-Einstein condensates loaded onto moiré optical lattices
Gap solitons and vortices in two-dimensional spin-orbit-coupled Bose-Einstein condensates loaded onto moiré optical lattices Open
In ultracold atomic gases, optical lattices and spin-orbit coupling are two important and useful linear means to study and control the nonlinear and quantum dynamics of matter waves, and both have been well realized in experiments. Here, n…
View article: Breather gas and shielding for the focusing nonlinear Schrödinger equation with nonzero backgrounds
Breather gas and shielding for the focusing nonlinear Schrödinger equation with nonzero backgrounds Open
Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow \inf…
The focusing complex mKdV equation with nonzero background: Large $N$-order asymptotics of multi-rational solitons and related Painlevé-III hierarchy Open
In this paper, we investigate the large-order asymptotics of multi-rational solitons of the focusing complex modified Korteweg-de Vries (c-mKdV) equation with nonzero background via the Riemann-Hilbert problems. First, based on the Lax pai…
Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ? Open
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 training of an artificial neural network can be converted to t…
Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons Open
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators …
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations Open
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Sp…
Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative Open
We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its Lévy index (LI). This FDNLS equation represents a nov…
View article: Dissipative gap solitons and vortices in moiré optical lattices
Dissipative gap solitons and vortices in moiré optical lattices Open
Considerable attention has been recently paid to elucidation the linear, nonlinear and quantum physics of moiré patterns because of the innate extraordinary physical properties and potential applications. Particularly, moiré superlattices …
The Sasa–Satsuma equation with high-order discrete spectra in space-time solitonic regions: soliton resolution via the mixed -Riemann–Hilbert problem Open
In this paper, we investigate the Cauchy problem of the Sasa–Satsuma (SS) equation with initial data belonging to the Schwartz space. The SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation an…
Rogue wave excitations and hybrid wave structures of the Heisenberg ferromagnet equation with time-dependent inhomogeneous bilinear interaction and spin-transfer torque Open
In this paper, we focus on the localized rational waves of the variable-coefficient Heisenberg spin chain equation, which models the local magnetization in ferromagnet with time-dependent inhomogeneous bilinear interaction and spin-transfe…
Large-space and long-time asymptotic behaviors of $N_{\infty}$-soliton solutions (soliton gas) for the focusing Hirota equation Open
The Hirota equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation, and can describe the ultra-short optical pulse propagation in the form $iq_t+α(q_{xx}+ 2|q|^2q)+iβ(q_{xxx}+ 6|q|^2q_x)=0,\, (x,t)\i…
Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones Open
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. Abundant data-driven solu…
Deep learning soliton dynamics and complex potentials recognition for 1D and 2D PT-symmetric saturable nonlinear Schrödinger equations Open
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 Schrödinger equations (SNLSEs) with two fundamental PT-symmetric Sca…
Well-posedness of scattering data for the derivative nonlinear Schrödinger equation in $H^s(\mathbb{R})$ Open
We prove the well-posedness results of scattering data for the derivative nonlinear Schrödinger equation in $H^{s}(\mathbb{R})(s\geq\frac12)$. We show that the reciprocal of the transmission coefficient can be written as the sum of some it…
Spontaneous symmetry breaking and ghost states in two-dimensional fractional nonlinear media with non-Hermitian potential Open
The interaction of fractional diffraction and parity-time ( $${{{{{\mathcal{PT}}}}}}$$ ) symmetric would bring some unique properties to certain physical system. Here we report a spontaneous symmetry breaking (SSB) phenomenon and ghost sta…
Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential Open
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 Lee-Huang-Yang corrections. In particular, exact QD states a…
Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential Open
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 nonlinearity and PT-symmetric potential. The continuous as…
New Integrable Multi-Lévy-Index and Mixed Fractional Nonlinear Soliton Hierarchies Open
In this letter, we present a simple and new idea to generate two types of novel integrable multi-Lévy-index and mix-Lévy-index (mixed) fractional nonlinear soliton hierarchies, containing multi-index and mixed fractional higher-order nonli…
Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator Open
In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the soliton mapping between two function spaces, where one is the fractional-order index space $\{ε|ε\in (0, 1)\}$ in the fractional integrable nonlinear wave …
Interactions of fractional N-solitons with anomalous dispersions for the integrable combined fractional higher-order mKdV hierarchy Open
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 combined fractional higher-order mKdV (fhmKdV) hierarchy, i…
Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations Open
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrodinger (fHONLS) equations, containing the fractional Hir…
Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons Open
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 via the deep neural networks leaning. Moreover, the inverse …
View article: The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities
The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities Open
This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH…
Data-driven discovery of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes. Open
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.…
Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes Open
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. …
Parity-time-symmetric rational vector rogue waves of the <i>n</i>-component nonlinear Schrödinger equation Open
Extreme events are investigated in the integrable n-component nonlinear Schrödinger (NLS) equation with focusing nonlinearity. We report novel multi-parametric families of rational vector rogue wave (RW) solutions featuring the parity-time…