This paper is devoted to the unique global admissible conservative solutions of the periodic dispersive Hunter–Saxton equation. Using the standard ordinary differential equation theory, we first get the global admissible conservative solutions of the periodic dispersive Hunter–Saxton equation. Then, given an admissible conservative solution $u(t,x)$, an equation is introduced which singles out a unique characteristic curve through each initial point. Finally, by building an ordinary differential equation system, we get the uniqueness of the global admissible conservative solutions without any additional assumptions.

中文翻译：

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周期色散Hunter-Saxton方程的整体保守解

本文致力于周期色散Hunter-Saxton方程的唯一全局可容许保守解。使用标准的常微分方程理论，我们首先获得了周期色散Hunter-Saxton方程的全局容许保守解。然后，给出一个可接受的保守解$ü（Ť，X）$，引入了一个方程式，该方程式通过每个初始点都选择出唯一的特性曲线。最后，通过建立一个常微分方程组，我们无需任何其他假设即可获得全局可容许保守解的唯一性。