In this paper, we study the evolution scenarios of surfaces of revolution associated with the kink-type solutions of an integrable equation, which is called the SIdV equation because of its scale-invariant property and relationship with the Korteweg-de Vries equation, where the kink-type solutions play the role of a metric. We put forward two kinds of evolution scenarios for surfaces of revolution associated with two types of kink-type metric (solution) and we study the key properties of these surfaces.

中文翻译：

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与SIdV方程的扭结型解相关的旋转面

在本文中，我们研究了与可积方程的扭结型解相关的旋转表面的演化场景，由于其尺度不变性以及与Korteweg-de Vries方程的关系，因此将其称为SIdV方程。扭结型解决方案起着度量标准的作用。针对与两种扭结型度量（解决方案）相关的旋转曲面，我们提出了两种演化方案，并研究了这些曲面的关键特性。