Peakon-antipeakon interaction in the Dullin-Gottwald-Holm equation

In this Letter, we obtain a two-peakon solution to a special Dullin-Gottwald-Holm equation explicitly by direct computation, and then discuss the peakon-antipeakon interaction in this equation. Our results show that, like the Camassa-Holm equation, during the soliton absorption time, the peakon-antipeakon in this equation is essentially a single-peaked, double-cornered wave. However, the two corners may travel in opposite direction for some ω, which is different from that in the Camassa-Holm equation.