In this paper, we prove that the KAM tori for the generalized Boussinesq equation with the external parameters, which generates an infinite dimensional Hamiltonian system, are long-time stable. Precisely, we prove that the solutions with initial datum in the $\delta$-neighborhood of KAM torus still stay close to the KAM torus for $\left|t\right|\le {\delta }^{-\mathcal{M}}$ with $\mathcal{M}\ge 1$. The proof is based on constructing a partial normal form of higher order and showing that the $p$-tame property for the Hamiltonian vector field persists after the changes of variables of the KAM scheme and under normal form iterative procedure.

中文翻译：

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广义Boussinesq方程KAM tori的长时间稳定性。

在本文中，我们证明了带有外部参数的广义Boussinesq方程的KAM tori是长期稳定的，该方程可生成无限维哈密顿系统。精确地，我们证明了具有初始基准的解$\delta$-KAM圆环附近仍然保持靠近KAM圆环 $\left|Ť\right|\le {\delta }^{-\mathcal{中号}}$ 与 $\mathcal{中号}\ge \mathrm{1个}$。证明是基于构造较高阶的部分范式并显示出$p$哈密​​顿向量场的-tame属性在KAM方案的变量更改后并且在正常形式的迭代过程下仍然存在。