Forced waves of saturation type for Fisher–KPP equation in a shifting environment

In this paper, we study the forced waves of the Fisher-KPP equation in a shifting environment. We introduce a new method to construct a sub-solution to derive the existence of forced waves without the monotonicity assumption on the shifting growth rate function. The forced waves we derived here are of the saturation type, in contrast to the extinction type in the literature (c) 2023 Elsevier Ltd. All rights reserved.