A proof that strong solutions of the Dullin–Gottwald–Holm equation vanishing on an open set of the (1 + 1) space-time are identically zero is presented. In order to do it, we use a geometrical approach based on the conserved quantities of the equation to prove a unique continuation result for its solutions. We show that this idea can be applied to a large class of equations of the Camassa–Holm type.

中文翻译：

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一些浅水模型的守恒量、延拓和紧支解

证明了在 (1 + 1) 时空的开集上消失的 Dullin-Gottwald-Holm 方程的强解完全为零。为了做到这一点，我们使用基于方程守恒量的几何方法来证明其解的唯一连续结果。我们表明这个想法可以应用于一大类 Camassa-Holm 类型的方程。