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

Abstract 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.