Publications (99)
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 admi…
Painlevé \uppercase\expandafter{\romannumeral34\relax} and collisionless shock in the defocusing NLS equation with step-like initial data in the transition regions
Engui Fan, Zhaoyu Wang, Yidan Zhang
We consider the Cauchy problem for the defocusing nonlinear Schrödinger (NLS) equation with step-like initial data. Using the nonlinear steepest descent method, we derive the long…
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…
Long-time asymptotic for the derivative nonlinear Schrödinger equation with step-like initial value
Jian Xu, Engui Fan
We consider the Cauchy problem for the Gerdjikov-Ivanov(GI) type of the derivative nonlinear Schrödinger (DNLS) equation: with…
Long time asymptotics for the nonlocal mKdV equation with finite density initial data
Xuan Zhou, Engui Fan
In this paper, we consider the Cauchy problem for an integrable real nonlocal (also called reverse-space-time) mKdV equation with nonzero boundary conditions \begin{align*} &q_t(x,…
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…
Long time asymptotics for the focusing nonlinear Schrödinger equation in the solitonic region with the presence of high-order discrete spectrum
Zhaoyu Wang, Meisen Chen, Engui Fan
In this paper, we use the steepest descent method to study the initial value problem for focusing nonlinear Schrödinger (fNLS) equation with non-generic weighted…
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…
Perturbed Hankel determinant, correlation functions and Painlevé equations
Min Chen, Yang Chen, Engui Fan
We continue with the study of the Hankel determinant, generated by a Pollaczek-Jacobi type w…
On Negative Order KdV Equations
Zhijun Qiao, Engui Fan
In this paper, based on the regular KdV system, we study negative order KdV (NKdV) equations about their Hamiltonian structures, Lax pairs, infinitely many conservation laws, and e…
Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems
Meisen Chen, Engui Fan, Jingsong He
In this paper, we establish -Sobolev space bijectivity of the inverse scattering transform related to the defocusing Ablowitz-Ladik system. On the one hand, in the direct prob…
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., $…
The Fokas-Lenells equation on the line: Global well-posedness with solitons
Qiaoyuan Cheng, Engui Fan
In this paper, we prove the existence of global solutions in to the Fokas-Lenells (FL) equation on the line when the initial data includes…
Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with initial potential in weighted sobolev space
Meisen Chen, Engui Fan
In this paper, we are going to investigate Cauchy problem for nonlocal nonlinear Schrödinger equation with the initial potential in weighted sobolev space $H^{1,1}(\mathb…
Long time asymptotic behavior for the nonlocal mKdV equation in space-time solitonic regions-II
Xuan Zhou, Engui Fan
We study the long time asymptotic behavior for the Cauchy problem of an integrable real nonlocal mKdV equation with nonzero initial data in the solitonic regions \begin{align*} &q_…
On the asymptotic stability of -soliton solutions of the three-wave resonant interaction equation
Yiling Yang, Engui Fan
The three-wave resonant interaction (three-wave) equation not only possesses matrix spectral problem, but also being absence of stationary phase points, which give rise…
On the global existence for the modified Camassa-Holm equation via the inverse scattering method
Yiling Yang, Engui Fan, Yue Liu
In this paper, we address the existence of global solutions to the Cauchy problem of the modified Camassa-Holm (mCH) equation, which is known as a model for the unidirectional prop…
A Riemann-Hilbert approach to existence of global solutions to the Fokas-Lenells equation on the line
Qiaoyuan Cheng, Engui Fan
We obtain the the existence of global solutions to the Cauchy problem of the Fokas-Lenells (FL) equation on the line \begin{align} &u_{xt}+αβ^2u-2iαβu_x-αu_{xx}-iαβ^2|u|^2u_…
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_…
Algebro-geometric solutions and their reductions for the Fokas-Lenells hierarchy
Peng Zhao, Engui Fan, Yu Hou
This paper is dedicated to provide theta function representations of algebro-geometric solutions for the Fokas-Lenells (FL) hierarchy through studying an algebro-geometric initial…
Existence of global solutions for the modified Camassa-Holm equation with a nonzero background
Yiling Yang, Engui Fan, Yue Liu
Consideration in the present paper is the existence of global solutions for the modified Camassa-Holm (mCH) equation with a nonzero background initial value. The mCH equation is co…
Existence of global solutions to the nonlocal Schrödinger equation on the line
Yi Zhao, Engui Fan
In this paper, we address the existence of global solutions to the Cauchy problem for the integrable nonlocal nonlinear Schrödinger (nonlocal NLS) equation with the initial data $…
Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value
Jian Xu, Engui Fan
We present a new Riemann-Hilbert problem formalism for the initial value problem for the derivative nonlinear Schrödinger (DNLS) equation on the line. We show that the solution of…
The algebro-geometric solutions for the modified Camassa-Holm hierarchy
Yu Hou, Engui Fan, Zhijun Qiao
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the modified Camassa-Holm (MCH) hierarchy through…
Soliton resolution and asymptotic stability of -soliton solutions for the defocusing mKdV equation with a non-vanishing background
Zechuan Zhang, Taiyang Xu, Engui Fan
We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg-de Vries (mKdV) equation under a symmetric non-vanishing background, which supp…
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…
Binary Bell polynomials approach to the integrability of nonisospectral and variable-coefficient nonlinear equations
Engui Fan
Recently, Lembert, Gilson et al proposed a lucid and systematic approach to obtain bilinear Bäcklund transformations and Lax pairs for constant-coefficient soliton equations based…
The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy
Peng Zhao, Engui Fan, Yu Hou
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tool…
Long-time Asymptotics for the Ablowitz-Ladik system with present of solitons
Meisen Chen, Engui Fan, Zhaoyu Wang
We investigate the soliton resolution and Painlevé asymptotics for the focusing Ablowitz-Ladik system with the initial data in a discrete weighted space. First, we establ…
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…
The coupled Schodinger hierarchy associated with third-order algebraic curves and algebro-geometric solutions
Yu Hou, Engui Fan
By introducing Lenard recursion equations, we derive a general coupled nonlinear Schdinger (CNLS) hierarchy associated with well-known Manakov system and Sasa-Sa…
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 (…
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-m…
Long-time asymptotic behavior of the Hunter-Saxton equation
Luman Ju, Kai Xu, Engui Fan
With -generalization of the Deift-Zhou steepest descent method, we investigate the long-time asymptotics of the solution to the Cauchy problem for the Hunter-Saxton…
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…
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 of a mixed schrödinger equation with weighted Sobolev initial data
Qiaoyuan Cheng, Yiling Yang, Engui Fan
We apply steepest descent method to obtain sharp asymptotics for a mixed schrödinger equation $$…
The Fokas method to the Sasa-Satsuma equation on the half-line
Jian Xu, Engui Fan
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the Sasa-Satsuma(SS) equation: $iq_T+\frac{1}{2}q_{XX}+|q|^2q+i\eps (q_{XXX}+6|q|^2q_X+3q(…
New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy
Peng Zhao, Engui Fan
We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hi…
Critical edge behavior in the singularly perturbed Pollaczek-Jacobi type unitary ensemble
Zhaoyu Wang, Engui Fan
In this paper, we study the strong asymptotic for the orthogonal polynomials and universality associated with singularly perturbed Pollaczek-Jacobi type weight $$w_{p_J2}(x,t)=e^{-…
The Algebro-Geometric Initial Value Problem for the Relativistic Lotka-Volterra Hierarchy and Quasi-Periodic Solutions
Peng Zhao, Engui Fan, Yu Hou
We provide a detailed treatment of relativistic Lotka-Volterra hierarchy and a kind of initial value problem with special emphasis on its the theta function representation of all a…
The derivative nonlinear Schrodinger equation on the interval
Jian Xu, Engui Fan
We use the Fokas method to analyze the derivative nonlinear Schrödinger (DNLS) equation on the interval . Assuming that the solution $q(x…
Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
Yuan Li, Qiaoyuan Cheng, Engui Fan
We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space .This resul…
Orbital Stability of Soliton for the Derivative Nonlinear Schrödinger Equation in the Space
Yiling Yang, Engui Fan, Yue Liu
In this paper, we establish the orbital stability of the 1-soliton solution for the derivative nonlinear Schrödinger equation under perturbations in . We demonstr…
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…
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…
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…
Bilinear approach to the quasi-periodic wave solutions of supersymmetric equations in superspace
Engui Fan
We devise a lucid and straightforward way for explicitly constructing quasi-periodic wave solutions (also called multi-periodic wave solutions) of supersymmetric equations in super…
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…
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…
Long-time asymptotics for the focusing Fokas-Lenells equation in the solitonic region of space-time
Qiaoyuan Cheng, Engui Fan
We study the long-time asymptotic behavior of the focusing Fokas-Lenells (FL) equation $$ u_{xt}+αβ^2u-2iαβu_x-αu_{xx}-iαβ^2|u|^2u_x=0 \label{cs} $$ with generic initial dat…
Leading-order temporal asymptotics of the Fokas-Lenells Equation without solitons
Jian Xu, Engui Fan
We use the Deift-Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas-Lenells equation as $t\ra+\infty$…
Generalized Super Bell Polynomials with Applications to Superymmetric Equations
Engui Fan, Y. C. Hon
In this paper, we introduce a class of new generalized super Bell polynomials on a superspace, explore their properties, and show that they are a natural and effective tool to syst…
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 w…
-Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations
Yuan Li, Xinhan Liu, Engui Fan
We consider the Cauchy problem to the general defocusing and focusing matrix nonlinear Schrödinger (NLS) equations with initial data allowing arbitrary-order poles and…
The algebro-geometric solutions for Degasperis-Procesi hierarchy
Yu Hou, Peng Zhao, Engui Fan +1
Though completely integrable Camassa-Holm (CH) equation and Degasperis-Procesi (DP) equation are cast in the same peakon family, they possess the second- and third-order Lax operat…
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 Schrdi…
Existence of global solutions for the nonlocal derivation nonlinear Schrödinger equation by the inverse scattering transform method
Yuan Li, Xinhan Liu, Engui Fan
We address the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schrödinger equation in weighted Sobolev space $H^{2}(\m…
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…
Existence of global solutions to the nonlocal mKdV equation on the line
Anran Liu, Engui Fan
In this paper, we address the existence of global solutions to the Cauchy problem for the integrable nonlocal modified Korteweg-de vries (nonlocal mKdV) equation with the initial d…
Local and global well-posedness for the nonlinear Schrödinger equation with nonhomogeneous boundary conditions
Engui Fan, Yuan Li, Xinhan Liu
In this paper, we study the initial-boundary value problem for the nonlinear Schrödinger equation in \begin{equation*} i\partial_{t}u+Îu+λ|u|^pu=0, \qquad (…
Painleve XXXIV asymptotics for the defocusing mKdV equation with step-like initial data in transition regions
Engui Fan, Zhaoyu Wang, Yidan Zhang
In this paper, we consider the Cauchy problem for the defocusing modified Korteweg-de Vries (mKdV) equation with a step-like initial data. Based on the Riemann-Hilbert problem asso…
The Cauchy problem for the Degasperis-Procesi Equation: Painlevé Asymptotics in Transition Zones
Zhaoyu Wang, Xuan Zhou, 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 an asymptotic approximation for the unidirection…
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_{…
The complex mKdV equation with step-like initial data: Large time asymptotic analysis
Zhaoyu Wang, Kai Xu, Engui Fan
In this paper, we study large-time asymptotics for the complex modified Korteveg-de Vries equation \begin{equation} u_t + \frac{1}{2}u_{xxx}+3|u|^2 u_x=0, \end{equation} with the s…
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,…
Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval
Qiaozhen Zhu, Jian Xu, Engui Fan
In this paper, we apply Fokas unified method to study initial-boundary value problems for the two-component Gerdjikov-Ivanov equation formulated on the finite interval with $3 \tim…
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…
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…
Explicit quasi-periodic wave solutions and asymptotic analysis to the supersymmetric Ito's equation
Engui Fan, Y. C. Hon
Based on a Riemann theta function and the super-Hirota bilinear form, we propose a key formula for explicitly constructing quasi-periodic wave solutions of the supersymmetric Ito's…
Long time asymptotic behavior for the nonlocal nonlinear Schrödinger equation with weighted Sobolev initial data
Gaozhan Li, Yiling Yang, Engui Fan
In this paper, we extend steepest descent method to study the Cauchy problem for the nonlocal nonlinear Schrödinger (NNLS) equation with weighted Sobolev initi…
The algebro-geometric solutions for Hunter-Saxton hierarchy
Yu Hou, Engui Fan, Peng Zhao
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying…
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 and Painleve-type asymptotics for the Sasa-Satsuma equation in solitonic space time regions
Weikang Xun, Engui Fan
The Sasa-Satsuma equation with Lax representation is one of the integrable extensions of the nonlinear Schrödinger equation. In this paper, we consider the Cauchy pr…
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…
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 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…
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…
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…
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…
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…
The Cauchy problem of the Camassa-Holm equation in a weighted Sobolev space: Long-time and Painlevé asymptotics
Kai Xu, Yiling Yang, Engui Fan
Based on the -generalization of the Deift-Zhou steepest descent method, we extend the long-time and Painlevé asymptotics for the Camassa-Holm (CH) equation to t…
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…
The unified method for the three-wave equation on the half-line
Jian Xu, Engui Fan
We present a Riemann-Hilbert problem formalism for the initial-boundary value problem for the three-wave equation: \[p_{ij,t}-\frac{b_i-b_j}{a_i-a_j}p_{ij,x}+\sum_k(\frac{b_k-b_j}{…
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…
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…
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_…
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…
On asymptotic approximation of the modified Camassa-Holm equation in different space-time solitonic regions
Yiling Yang, Engui Fan
In this paper, we study the long time asymptotic behavior for the initial value problem of the modified Camassa-Holm (mCH) equation in the solitonic region \begin{align} &m_{t}+\le…
The asymptotic stability of solitons in the focusing Hirota equation on the line
Ruihong Ma, Engui Fan
In this paper, the -steepest descent method and Bäcklund transformation are used to study the asymptotic stability of solitons to the Cauchy problem of focusing…
he Cauchy problem for the Novikov equation under a nonzero background: Painlevé asymptotics in a transition zone
Zhaoyu Wang, Xuan Zhou, Engui Fan
In this paper, we investigate the Painlevé asymptotics in a transition zone for the solutions to the Cauchy problem of the Novikov equation under a nonzero background \begin{align…
A Riemann theta function formula with its application to double periodic wave solutions of nonlinear equations
Engui Fan, Kwok Wing Chow
Based on a Riemann theta function and Hirota's bilinear form, a lucid and straightforward way is presented to explicitly construct double periodic wave solutions for both nonlinear…
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…
Painlevé XXXIV asymptotics for the defocusing nonlinear Schrödinger equation with a finite-genus algebro-geometric background
Engui Fan, Gaozhan Li, Yiling Yang +1
In this paper, we consider the Cauchy problem for the defocusing nonlinear Schrdinger equation with a finite genus algebro-geometric background. Long-time asymptot…
The defocusing NLS equation with nonzero background: Large-time asymptotics in the solitonless region
Zhaoyu Wang, Engui Fan
We consider the Cauchy problem for the defocusing Schrdinger (NLS) equation with a nonzero background $$\begin{align} &iq_t+q_{xx}-2(|q|^2-1)q=0, \nonumber\\ &q(x,…
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…
On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions
Taiyang Xu, Zechuan Zhang, Engui Fan
We investigate the long-time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data. The prese…
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}…
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…