5 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-…
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…
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 establi…
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…
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,…