We consider persistence properties of solutions for a generalised wave equation including vibration in elastic rods and shallow water models, such as the BBM, the Dai’s, the Camassa–Holm, and the Dullin–Gottwald–Holm equations, as well as some recent shallow water equations with Coriolis effect. We establish unique continuation results and exhibit asymptotic profiles for the solutions of the general class considered. From these results we prove the non-existence of non-trivial spatially compactly supported solutions for the equation. As an aftermath, we study the equations earlier mentioned in light of our results for the general class.

中文翻译：

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非线性波动方程解的持久性和渐近分析

我们考虑广义波动方程解的持久性特性，包括弹性杆和浅水模型的振动，例如 BBM、Dai、Camassa-Holm 和 Dullin-Gottwald-Holm 方程，以及一些最近的浅水方程具有科里奥利效应的方程。我们建立了独特的连续结果，并展示了所考虑的一般类别的解决方案的渐近轮廓。从这些结果中，我们证明了方程不存在非平凡的空间紧支持解。作为后果，我们根据普通班的结果研究前面提到的方程。