388 citations · 2.8k across the 44 of their papers we have counts for
44 papers
New Integrable Multi-Lévy-Index and Mixed Fractional Nonlinear Soliton Hierarchies
Zhenya Yan
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, con…
Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator
Ming Zhong, Zhenya Yan
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|…
Dynamics of fractional N-soliton solutions with anomalous dispersions of integrable fractional higher-order nonlinear Schrödinger equations
Weifang Weng, Minghe Zhang, Zhenya Yan
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Sc…
The Cauchy problem and wave-breaking phenomenon for a generalized sine-type FORQ/mCH equation
Guoquan Qin, Zhenya Yan, Boling Guo
In this paper, we are concerned with the Cauchy problem and wave-breaking phenomenon for a sine-type modified Camassa-Holm (alias sine-FORQ/mCH) equation. Employing the transport e…
Orbital stability of peakon solutions for a generalized higher-order Camassa-Holm equation
Guoquan Qin, Zhenya Yan, Boling Guo
In this paper, we investigate the orbital stability issue of a generalized higher-order Camassa-Holm (HOCH) equation, which is an higher-order extension of the quadratic CH equatio…
The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities
Guoquan Qina, Zhenya Yan, Boling Guo
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 generaliza…
Higher-dimensional soliton generation, stability and excitations of the PT-symmetric nonlinear Schrödinger equations
Yong Chen, Zhenya Yan, Boris A. Malomed
We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schrödinger…
Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue waves
Zijian Zhou, Zhenya Yan
The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wa…
Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
Guoqiang Zhang, Liming Ling, Zhenya Yan +1
The extreme events are investigated for an -component nonlinear Schrödinger (-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields. We…
Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
Zijian Zhou, Zhenya Yan
In this paper, we investigate the logarithmic nonlinear Schrödinger (LNLS) equation with the parity-time (PT)-symmetric harmonic potential, which is an important physical model in…
Inverse scattering transforms and N-double-pole solutions for the derivative NLS equation with zero/non-zero boundary conditions
Guoqiang Zhang, Zhenya Yan
We systematically report a rigorous theory of the inverse scattering transforms (ISTs) for the derivative nonlinear Schrodinger (DNLS) equation with both zero boundary condition (Z…
Inverse scattering transforms for the focusing and defocusing mKdV equations with nonzero boundary conditions
Guoqiang Zhang, Zhenya Yan
We explore systematically a rigorous theory of the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (m…
A unified inverse scattering transform and soliton solutions of the nonlocal modified KdV equation with non-zero boundary conditions
Guoqiang Zhang, Zhenya Yan
We present a rigorous theory of a unified and simple inverse scattering transform (IST) for both focusing and defocusing real nonlocal (reverse-space-time) modified Korteweg-de Vri…
Impact of near-PT symmetry on exciting solitons and interactions based on a complex Ginzburg-Landau model
Yong Chen, Zhenya Yan, Wenjun Liu
We present and theoretically report the influence of a class of near-parity-time-(PT-) symmetric potentials with spectral filtering parameter and nonlinear gain-loss coeffici…
Integrable -symmetric local and nonlocal vector nonlinear Schrödinger equations: a unified two-parameter model
Zhenya Yan
We introduce a new unified two-parameter wave model (simply called model), connecting integrable local and nonlocal v…
A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations
Zhenya Yan
We use two families of parameters to first introduce a unified novel two-family-parameter system (simply called ${\math…
Long-time asymptotics for initial-boundary value problems of integrable Fokas-Lenells equation on the half-line
Shuyan Chen, Zhenya Yan
We study the Schwartz class of initial-boundary value (IBV) problems for the integrable Fokas-Lenells equation on the half-line via the Deift-Zhou's nonlinear descent method analys…
Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
Zichao Wen, Zhenya Yan
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schroedinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and period…
An initial-boundary value problem of the general three-component nonlinear Schrodinger equation with a 4x4 Lax pair on a finite interval
Zhenya Yan
We investigate the initial-boundary value problem for the general three-component nonlinear Schrodinger (gtc-NLS) equation with a 4x4 Lax pair on a finite interval by extending the…
An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4x4 Lax pair on the half-line
Zhenya Yan
We investigate the initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii (GP) equations with a 4x4 Lax pair on the half-line. The solution of this system can be…
On stable solitons and interactions of the generalized Gross-Pitaevskii equation with PT-and non-PT-symmetric potentials
Zhenya Yan, Yong Chen, Zichao Wen
We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time-(PT-) and non-PT-symmetric potentials. We find th…
Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
Yong Chen, Zhenya Yan
The effect of derivative nonlinearity and parity-time- (PT-) symmetric potentials on the wave propagation dynamics is investigated in the derivative nonlinear Schrodinger equation,…
Localized Analytical Solutions and Parameters Analysis in the Nonlinear Dispersive Gross-Pitaevskii Mean-Field GP (m,n) Model with Space-Modulated Nonlinearity and Potential
Zhenya Yan
The novel nonlinear dispersive Gross-Pitaevskii (GP) mean-field model with the space-modulated nonlinearity and potential (called GP(m, n) equation) is investigated in this paper.…
Generalized perturbation (n, M)-fold Darboux transformations and multi-rogue-wave structures for the modified self-steepening nonlinear Schrodinger equation
Xiao-Yong Wen, Yunqing Yang, Zhenya Yan
In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of the modified nonlinear Schrodinger (MN…