78 citations · 365 across the 100 of their papers we have counts for
9 papers · 1 filter
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}…
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 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…
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…
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}(\ma…
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…
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…
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…
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…