In this paper, we study the existence and bifurcation of peakon and anti-peakon to the [Formula: see text]-degree [Formula: see text]-equation with [Formula: see text] and positive integer [Formula: see text]. Using qualitative theory and bifurcation method of dynamical systems, for positive wave speed we confirm the following properties: (1) When [Formula: see text], the equation has peakon, but no anti-peakon. (2) When [Formula: see text], the equation has not only peakon but also anti-peakon. There is a bifurcation wave speed for peakon and anti-peakon. (3) When [Formula: see text] is even, there exists a maximum wave speed for peakon. (4) When [Formula: see text] is odd, there is no maximum wave speed for peakon.
On an encounter of two men of mathematics in Lima
