5 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…
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…
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…
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 establ…