Exact solutions for chemical concentration waves of self-propelling camphor particles racing on a ring: A novel potential dynamics perspective

A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are derived. The bifurcation diagram describing the transition between the immobile and self-propelling modes of camphor objects is derived semi-analytically. The bifurcation is of a pitchfork type which is consistent with earlier theoretical work in which natural boundary conditions have been considered.