Abstract We study an integro-difference equation that describes the spatial dynamics of a species in a shifting habitat. The growth function is nondecreasing in density and space for a given time, and shifts at a constant speed c. The spreading speeds for the model were previously studied. The contribution of the current paper is to provide sharp conditions for existence of forced traveling waves with speed c. We show the existence of traveling waves with zero value at ∞ or −∞ for c in different value ranges determined by the spreading speeds. We also show the existence of a traveling wave with any speed c for the case that the species can grow everywhere. Our results demonstrate the existence of different types of traveling waves with the same speed.

中文翻译：

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具有移动栖息地的积分差分方程中的行波

摘要 我们研究了一个积分差分方程，该方程描述了一个物种在不断变化的栖息地中的空间动态。增长函数在给定时间内密度和空间不减少，并以恒定速度 c 移动。先前研究了模型的铺展速度。当前论文的贡献是为速度为 c 的强迫行波的存在提供了尖锐的条件。我们展示了在由传播速度确定的不同值范围内对于 c 在 ∞ 或 -∞ 处存在零值的行波。对于物种可以随处生长的情况，我们还展示了具有任何速度 c 的行波的存在。我们的结果表明存在具有相同速度的不同类型的行波。