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math.AP2024
The Cauchy problem for the Degasperis-Procesi Equation: Painlevé Asymptotics in Transition Zones
Zhaoyu Wang, Xuan Zhou, 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 an asymptotic approximation for the unidirectiona…
math.AP2023
he Cauchy problem for the Novikov equation under a nonzero background: Painlevé asymptotics in a transition zone
Zhaoyu Wang, Xuan Zhou, Engui Fan
In this paper, we investigate the Painlevé asymptotics in a transition zone for the solutions to the Cauchy problem of the Novikov equation under a nonzero background \begin{align}…
math.AP2021
Long time asymptotics for the focusing nonlinear Schrödinger equation in the solitonic region with the presence of high-order discrete spectrum
Zhaoyu Wang, Meisen Chen, Engui Fan
In this paper, we use the steepest descent method to study the initial value problem for focusing nonlinear Schrödinger (fNLS) equation with non-generic weighted S…