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…