15 papers
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+Îu+λ|u|^pu=0, \qquad (…
Painlevé XXXIV Asymptotics for the Focusing mKdV Equation with Finite-Genus Background and Discrete Spectrum
Ruihong Ma, Engui Fan
We investigate the Cauchy problem for the focusing modified Korteweg--de Vries (mKdV) equation with finite-genus algebro-geometric quasi-periodic initial data. By applying the nonl…
Painlevé Asymptotics of the Focusing Nonlinear Schrödinger Equation with a Finite-Genus Algebro-Geometric Background
Ruihong ma, Engui Fan
We investigate the Cauchy problem for the focusing nonlinear Schrödinger (NLS) equation \begin{equation} iq_t(x,t)+q_{xx}(x,t)+2|q(x,t)|^2q(x,t)=0,\quad x\in\mathbb{R},\quad t\ge0…
A dense focusing Ablowitz-Ladik soliton gas and its asymptotics
Meisen Chen, Engui Fan, Zhaoyu Wang +2
In this paper, we propose a soliton gas solution for the focusing Ablowitz-Ladik system. This solution is defined as the large N limit of the N-soliton solution, and arises from a…