We explicitly construct the analogue of the d’Alembert solution to the 1+1 wave equation in an hyperboloidal setting. This hyperboloidal d’Alembert solution is used, in turn, to gain intuition into the behaviour of solutions to the wave equation in a hyperboloidal foliation and to explain an apparently anomalous permanent displacement of the solution in numerical simulations discussed in the literature.

中文翻译：

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双曲面叶状结构中的达朗贝尔解

我们在双曲面设置中明确构造 1+1 波动方程的达朗贝尔解的模拟。反过来，使用双曲面达朗贝尔解可以直观地了解双曲面叶状结构中波动方程解的行为，并解释文献中讨论的数值模拟中解的明显异常永久位移。