Pulsating type entire solutions originating from three fronts for a bistable reaction–advection–diffusion equation in periodic media

Abstract

The present paper is to study the pulsating type entire solutions of a reaction–advection–diffusion equation in periodic media with bistable nonlinearity. It is well-known that the equation has three different types of pulsating traveling wavefronts: a bistable front and two families of monostable fronts. The existence of entire solutions originating from two different types of those fronts has also been established by Bu et al. (2016).It is natural to ask whether there are entire solutions originating from three fronts. In this paper, we construct two different types of pulsating entire solutions with merging three fronts. These entire solutions behave as t→−∞ like a monostable and bistable pulsating fronts coming from opposite directions and like another monostable pulsating front between these two fronts.