388 citations · 2.8k across the 44 of their papers we have counts for
22 papers · 1 filter
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…
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…
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…
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…
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…
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…
Dynamics of higher-order rational solitons for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time-symmetric potential
Xiao-Yong Wen, Zhenya Yan, Yunqing Yang
The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is a…
Nonlocal general vector nonlinear Schroedinger equations:Integrability, PT symmetribility, and solutions
Zhenya Yan
A family of new one-parameter (ε_x=\pm 1) nonlinear wave models (called G_{ε_x}^{(nm)} model) is presented, including both the local (ε_x=1) and new integrable nonlocal …
Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: exact solutions and stability
Xiao-Yong Wen, Zhenya Yan, Boris A. Malomed
An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational in…
Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrodinger equation with modulating coefficients
Zhenya Yan, Chaoqing Dai
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play impor…
Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates
Zhenya Yan, V. V. Konotop, A. V. Yulin +1
We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for e…
Nonautonomous discrete rogue waves and interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients
Zhenya Yan, Dongmei Jiang, W. M. Liu
We analytically investigate the nonautonomous discrete rogue wave solutions and their interaction in the generalized Ablowitz-Ladik-Hirota lattice with variable coefficients, which…
Three-dimensional rogue waves in non-stationary parabolic potentials
Zhenya Yan, V. V. Konotop, N. Akhmediev
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation w…
Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
Zhenya Yan
The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schrödinger equation with variable coefficients in terms of rational-like functions by using the si…
Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation
Zhenya Yan, Chao Hang
We provide analytical three-dimensional bright multi-soliton solutions to the (3+1)-dimensional Gross-Pitaevskii (GP) equation with time and space-dependent potential, time-depende…