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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 unidirection…
math.AP2024
-Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations
Yuan Li, Xinhan Liu, Engui Fan
We consider the Cauchy problem to the general defocusing and focusing matrix nonlinear Schrödinger (NLS) equations with initial data allowing arbitrary-order poles and…