Soliton resolution and asymptotic stability of $N$-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…