A Dispersive Regularization for the Modified Camassa--Holm Equation
A Dispersive Regularization for the Modified Camassa--Holm Equation
In this paper, we present a dispersive regularization approach to construct a global $N$-peakon weak solution to the modified Camassa--Holm equation (mCH) in one dimension. In particular, we perform a double mollification for the system of ODEs describing trajectories of $N$-peakon solutions and obtain $N$ smoothed peakons without collisions. Though …