78 citations · 365 across the 100 of their papers we have counts for
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Painlevé XXXIV Asymptotics for the Focusing mKdV Equation with Finite-Genus Background and Discrete Spectrum
Ruihong Ma, Engui Fan
We investigate the Cauchy problem for the focusing modified Korteweg--de Vries (mKdV) equation with finite-genus algebro-geometric quasi-periodic initial data. By applying the nonl…
Painlevé Asymptotics of the Focusing Nonlinear Schrödinger Equation with a Finite-Genus Algebro-Geometric Background
Ruihong ma, Engui Fan
We investigate the Cauchy problem for the focusing nonlinear Schrödinger (NLS) equation \begin{equation} iq_t(x,t)+q_{xx}(x,t)+2|q(x,t)|^2q(x,t)=0,\quad x\in\mathbb{R},\quad t\ge0,…
A dense focusing Ablowitz-Ladik soliton gas and its asymptotics
Meisen Chen, Engui Fan, Zhaoyu Wang +2
In this paper, we propose a soliton gas solution for the focusing Ablowitz-Ladik system. This solution is defined as the large N limit of the N-soliton solution, and arises from a…
Soliton resolution, asymptotic stability and Painlevé transcendents in the combined Wadati-Konno-Ichikawa and short-pulse equation
Yidan Zhang, Engui Fan
In this paper, we develop a Riemann-Hilbert (RH) approach to the Cauchy problem for the combined Wadati-Konno-Ichikawa and short-pulse (WKI-SP) equation. The solution of the Cauchy…
Riemann-Hilbert approach to the Algebro-Geometric solution of the modified Camassa-Holm equation with linear dispersion term
Engui Fan, Gaozhan Li, Yiling Yang
This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in genus. To achieve this…
Soliton Shielding of the focusing modified KdV equation
Ruihong Ma, Engui Fan
We consider soliton gas solutions of the modified Korteweg-de Vries (mKdV) equation, where the point spectrum of the condensate is located within a bounded domain in the upper half…
A Riemann-Hilbert approach to the two-component modified Camassa-Holm equation
Kai Xu, Luman Ju, Engui Fan
In this paper, we develop a Riemann-Hilbert (RH) approach to the Cauchy problem for the two-component modified Camassa-Holm (2-mCH) equation based on its Lax pair. Further via a se…
Soliton resolution and asymptotic stability of -loop-soliton solutions for the Ostrovsky-Vakhnenko equation
Ruihong Ma, Engui Fan
The Ostrovsky-Vakhnenko (OV) equation \begin{align*} &u_{txx}-3κu_x+3u_xu_{xx}+uu_{xxx}=0 \end{align*} is a short wave model of the well-known Degasperis-Procesi equation and admit…
The Painlevé-type asymptotics of defocusing complex mKdV equation with finite density initial data
Lili Wen, Engui Fan
We consider the Cauchy problem for the defocusing complex mKdV equation with finite density initial data \begin{align*} &q_t+\frac{1}{2}q_{xxx}-3|q|^2q_{x}=0,\\ &q(x,0)=q_{0}(x) \s…
Painlevé transcendents in the defocusing mKdV equation with non-zero boundary conditions
Zhaoyu Wang, Taiyang Xu, Engui Fan
We consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with non-zero boundary conditions \begin{align} &q_t(x,t)-6q^2(x,t)q_{x}(x,t)+q_{xxx}(x…
Soliton resolution and asymptotic stability of -solitons to the Degasperis-Procesi equation on the line
Xuan Zhou, Zhaoyu Wang, Engui Fan
The Degasperis-Procesi (DP) equation \begin{align} &u_t-u_{txx}+3κu_x+4uu_x=3u_x u_{xx}+uu_{xxx}, \nonumber \end{align} serving as a model delineating the propagation of shallow wa…
The defocusing NLS equation with nonzero background: Painlevé asymptotics in two transition regions
Zhaoyu Wang, Engui Fan
In this paper, we address the Painlevé aymptotics in the transition region to the Cauchy problem of the defocusing Schrding…
Large-time asymptotics to the focusing nonlocal modified Kortweg-de Vries equation with step-like boundary conditions
Taiyang Xu, Engui Fan
We investigate the large-time asymptotics of solution for the Cauchy problem of the nonlocal focusing modified Kortweg-de Vries (MKdV) equation with step-like initial data, i.e., $…
Painleve-type asymptotics for the defocusing Hirota equation in transition region
Weikang Xun, Luman Ju, Engui Fan
We consider the Cauchy problem for the classical Hirota equation on the line with decaying initial data. Based on the spectral analysis of the Lax pair of the Hirota equation, we f…
Long-time asymptotic behavior for the Novikov equation in solitonic regions of space time
Yiling Yang, Engui Fan
In this paper, we study the long time asymptotic behavior for the Cauchy problem of the Novikov equation with matrix spectral problem \begin{align} &u_{t}-u_{txx}+4 u_{…
Asymptotic Gap Probability Distributions of the Gaussian Unitary Ensembles and Jacobi Unitary Ensembles
Shulin Lyu, Yang Chen, Engui Fan
In this paper, we address a class of problems in unitary ensembles. Specifically, we study the probability that a gap symmetric about 0, i.e. is found in the Gaussian unit…
Long-time asymptotic behavior for the complex short pulse equation
Jian Xu, Engui Fan
In this paper, we consider the initial value problem for the complex short pulse equation with a Wadati-Konno-Ichikawa type Lax pair. We show that the solution to the initial value…
Critical edge behavior in the perturbed Laguerre ensemble and the Painleve V transcendent
Min Chen, Yang Chen, Engui Fan
In this paper, we consider the perturbed Laguerre unitary ensemble described by the weight function of with The Deif…
Large n-limit for Random matrices with External Source with 3 eigenvalues
Jian Xu, Engui Fan, Yang Chen
In this paper, we analyze the large n-limit for random matrix with external source with three distinct eigenvalues. And we confine ourselves in the Hermite case and the three disti…
Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations
Engui Fan, Manwai Yuen
For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x,y,z. In this paper, the Clarkson-Kruskal reduction method is…