Entire solutions originating from semi-trivial pulsating fronts of reaction–advection–diffusion competition systems in periodic media.

This paper is concerned with some new entire solutions of the reaction–advection–diffusion competition system in periodically varying media. It has been shown in an earlier work that such a system admits some pulsating front-like entire solutions. In this work, we construct some new entire solutions originating from semi-trivial pulsating fronts and investigate some propagation properties of these entire solutions. More precisely, we first construct a family of entire solutions originating from a single front, which propagate with the speed same to that of the front. Then, we construct some entire solutions originating from two different fronts at both sides, which behave as the two fronts propagating from both directions or one direction of the x -axis, and propagate with the speed between those of the two fronts. Finally, we give some numerical simulations to describe the propagation of these entire solutions. These kinds of entire solutions provide some new spreading ways other than pulsating fronts and front-like entire solutions for two competing species in a heterogeneous media. • The novelty lies in the construction of various appropriate sub-super-solutions. • This is the first work to construct semi-trivial entire solutions. • These entire solutions provide new spreading ways for two competing species. [ABSTRACT FROM AUTHOR]