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math.AP2026
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-…
math.AP2026
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…