78 citations · 365 across the 100 of their papers we have counts for
4 papers · 2 filters
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…
Local and global well-posedness for the nonlinear Schrödinger equation with nonhomogeneous boundary conditions
Engui Fan, Yuan Li, Xinhan Liu
In this paper, we study the initial-boundary value problem for the nonlinear Schrödinger equation in \begin{equation*} i\partial_{t}u+Δu+λ|u|^pu=0, \qquad (x,…
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…