Preprint 2006-011
Global Conservative Multipeakon Solutions of the Camassa–Holm Equation
Helge Holden and Xavier Raynaud
Abstract: We show how to construct globally defined multipeakon solutions of the Camassa–Holm equation. The construction includes in particular the case with peakon-antipeakon collisions. The solutions are conservative in the sense that the associated energy is constant for almost all times. Furthermore, we construct a new set of ordinary differential equations that determines the multipeakons globally. The system remains globally well-defined.