78 citations · 365 across the 100 of their papers we have counts for
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On the long-time asymptotics of the modified Camassa-Holm equation with step-like initial data
Yiling Yang, Gaozhan Li, Engui Fan
We study the long time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation with step-like initial data \begin{align} &m_{t}+\left(m\left(u^{2}-u_…
Multiple-high-order pole solutions for the NLS equation with quartic terms
Li-Li Wen, En-Gui Fan, Yong Chen
The aim of this article is to investigate the multiple-high-order pole solutions to the focusing NLS equation with quartic terms(QNLS) under the non-vanishing boundary conditions(N…
Long time asymptotic behavior for the derivative Schrödinger equation with nonzero boundary conditions
Yiling Yang, Qiaoyuan Cheng, Engui Fan
In this paper, we apply steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with nonzero boundary conditions \…
Inverse scattering transform and multiple high-order pole solutions for the Gerdjikov-Ivanov equation under the zero/nonzero background
Zhang Zechuan, Fan Engui
In this article, the inverse scattering transform is considered for the Gerdjikov-Ivanov equation with zero and non-zero boundary conditions by a matrix Riemann-Hilbert (RH) method…
Soliton Resolution for the Short-pluse Equation
Yiling Yang, Engui Fan
In this paper, we study the Cauchy problem for the focusing nonlinear short-pluse equation by using steepest descent method. \begin{align} &u_{xt}=u+\frac{1}{6}…
Inverse scattering transformation for the Fokas-Lenells equation with nonzero boundary conditions
Yi Zhao, Engui Fan
In this article, we focus on the inverse scattering transformation for the Fokas-Lenells (FL) equation with nonzero boundary conditions via the Riemann-Hilbert (RH) approach. Based…
The Sasa-Satsuma equation with non-vanishing boundary conditions
Lili Wen, Engui Fan
We concentrate on inverse scattering transformation for the Sasa-Satsuma equation with matrix spectral and nonzero boundary condition in this article. To circumvent mul…
Long-time asymptotic behavior of the modified Schrödinger equation via Dbar-steepest descent method
Yiling Yang, Engui Fan
In this paper, we consider the Cauchy problem for the modified NLS equation. Using nonlinear steepest descent method and combining the Dbar-analysis, we show that inside any fixed…
Long time asymptotics behavior of the focusing nonlinear Kundu-Eckhaus equation
Ruihong Ma, Engui Fan
We study the Cauchy problem for the focusing nonlinear Kundu-Eckhaus equation and construct long time asymptotic expansion of its solution in fixed space-time cone with $C(x_1,x_2,…
Long-time asyptotics behavior for the integrable modified Camassa-Holm equation with cubic nonlinearity
Jian Xu, Engui Fan
In this paper, we investigate the long-time asymptotic behavior of the solution to the initial value problem for the modified Camassa-Holm (mCH) equation with cubic nonlinearity. T…
The Riemann-Hilbert approach to focusing Kundu-Eckhaus equation with nonzero boundary conditions
Lili Wen, Engui Fan
In this article, we focus on investigating the focusing Kundu-Eckhaus equation with nonzero boundary condition. A appropriate two-sheeted Riemann surface is introduced to map the s…
Riemann-Hilbert approach to the modified nonlinear Schröinger equation with non-vanishing asymptotic boundary conditions
Yiling Yang, Engui Fan
The modified nonlinear Schrödinger (NLS) equation was proposed to describe the nonlinear propagation of the Alfven waves and the femtosecond optical pulses in a nonlinear single-mo…
Long-time asymptotics for the Nonlocal mKdV equation
Fengjing He, Engui Fan, Jian Xu
In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_…
Hankel determinants for a perturbed Laguerre weight and Painleve V equation
Min Chen, Yang Chen, Engui Fan
In this paper, we study Hankel determinants generated from a perturbed Laguerre weight function, Under the double scaling scheme, we give the uniform asymptotic approximations of H…
The unified transform method for the Sasa-Satsuma equation on the interval
Jian Xu, Qiaozhen Zhu, Engui Fan
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the Sasa-Satsuma(SS) equation on the finite interval. Assume that the solution existes, we…
The GLM representation of the global relation for the two-component nonlinear Schrödinger equation on the interval
Jian Xu, Engui Fan
In a previous work, we show that the solution of the initial-boundary value problem for the two-component nonlinear Schrödinger equation on the finite interval can be expressed in…
Initial-boundary value problem for integrable nonlinear evolution equations with Lax pairs on the interval
Jian Xu, Engui Fan
We present an approach for analyzing initial-boundary value problems which is formulated on the finite interval (, where is a positive constant) for integrable equ…
The Ostrovsky-Vakhnenko equation on the half-line: a Riemann-Hilbert approach
Jian Xu, Engui Fan
We analyze an initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line. This equation can be viewed as the short wave model for the Degasperis-Procesi (…
New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy
Peng Zhao, Engui Fan
We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hi…
Algebro-Geometric Solutions for the Kadomtsev-Petviashvili Hierarchy
Peng Zhao, Engui Fan
Based on the idea of symmetric constraint, we apply the Gesztesy-Holden's method to derive explicit representations of the Baker-Ahkiezer function of the KP hierarchy, from w…
A Riemann-Hilbert approach to the Harry-Dym equation on the line
Yu Xiao, Engui Fan
In this paper, we consider the Harry-Dym equation on the line with decaying initial value. The Fokas unified method is used to construct the solution of the Harry-Dym equation via…
Algebro-geometric solutions for the two-component Camassa-Holm Dym hierarchy
Yu Hou, Engui Fan
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Camassa-Holm Dym (CHD2) hierar…
Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy
Yu Hou, Engui Fan
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy…
Reality problems for the Algebro-Geometric Solutions of Fokas-Lenell hierarchy
Peng Zhao, Engui Fan
In a previous study, we obtained the algebro-geometric solutions and -dark solitons of Forkas-Lenells (FL) hierarchy using algebro-geometric method. In this paper, we construct…