In this paper, we focused on forced waves in the Leslie-Gower predator-prey system in shifting habitats with nonlocal dispersal. We demonstrated existence of two types of forced waves, namely, I: mixed front-pulse type forced waves, and II: front type forced waves. By applying the Schauder's fixed-point theorem and upper-lower solutions method, we established the existence of type I forced waves invading the state where only one species exists in both super-critical and critical cases. Besides, for any speed c, we proved the existence of type II forced waves invading the coexistence state using contracting rectangles methods. Particularly, due to the gradual deterioration of the environment over time, both predator and prey will eventually become extinct.
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Yang et al. (2024) studied this question.