71 citations · 133 across the 16 of their papers we have counts for
16 papers
Inverse scattering transform for the Kundu-Eckhaus Equation with nonzero boundary condition
Ning Guo, Jian Xu
In this paper, we consider the initial value problem for both of the defocusing and focusing Kundu-Eckhaus (KE) equation with non-zero boundary conditions (NZBCs) at infinity by in…
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…
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_…
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…
Long-time asymptotics for the short pulse equation
Jian Xu
In this paper, we analyze the long-time behavior of the solution of the initial value problem (IVP) for the short pulse (SP) equation. As the SP equation is a complete integrable s…
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…
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…
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 (…
Multi-hump solitary waves of nonlinear Dirac equation
Jian Xu, Sihong Shao, Huazhong Tang +1
This paper concentrates on a (1+1)-dimensional nonlinear Dirac (NLD) equation with a general self-interaction, being a linear combination of the scalar, pseudoscalar, vector and ax…
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 $t\ra+\infty$…
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}{…
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(…
Numerical methods for nonlinear Dirac equation
Jian Xu, Sihong Shao, Huazhong Tang
This paper presents a review of the current state-of-the-art of numerical methods for nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+1)-dimensio…
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,…