78 citations · 365 across the 100 of their papers we have counts for
13 papers · 1 filter
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,…
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 initia…
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 pro…
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,…
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…
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 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…
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_{…
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 S…
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}(\mathbb…
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 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…
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 \…