Peakons and Persistence Properties of Solution for the Interacting System of Popowicz

Abstract

This paper focuses on a two-component interacting system introduced by Popowicz, which has the coupling form of the Camassa–Holm and Degasperis–Procesi equations. Using distribution theory, single peakon solutions and several double peakon solutions of the system are described in an explicit expression. Moreover, dynamic behaviors of several types of double peakon solutions are illustrated through figures. In addition, the persistence properties of the solutions to the Popowicz system in weighted Lp spaces is considered via a large class of moderate weights.

Keywords

• Camassa–Holm and Degasperis–Procesi equations
• distribution theory
• peakon–solutions
• persistence property