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math-ph2023
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…
math-ph2022
Soliton resolution and asymptotic stability of -solitons to the Degasperis-Procesi equation on the line
Xuan Zhou, Zhaoyu Wang, Engui Fan
The Degasperis-Procesi (DP) equation \begin{align} &u_t-u_{txx}+3κu_x+4uu_x=3u_x u_{xx}+uu_{xxx}, \nonumber \end{align} serving as a model delineating the propagation of shallow wa…
math-ph2022
The defocusing NLS equation with nonzero background: Painlevé asymptotics in two transition regions
Zhaoyu Wang, Engui Fan
In this paper, we address the Painlevé aymptotics in the transition region to the Cauchy problem of the defocusing Schrding…