10 citations · 48 across the 31 of their papers we have counts for
13 papers · 1 filter
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-…
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…
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…
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 unidirectiona…
-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…
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}…