Abstract In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove that a heteroclinic orbit in the energy level 0 of a 2-dof Hamiltonian H e is destroyed giving rise to heteroclinic connections between certain elements (at infinity) for exponentially small (in e) energy levels. In this setting Melnikov theory does not apply because there are exponentially small phenomena.

中文翻译：

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扭结缺陷相互作用模型中的临界速度：严格的结果

摘要 在这项工作中，我们研究了具有弱缺陷的正弦-戈登方程的扭结相互作用模型。我们通过几何方法获得了关于 [7] 中导出的所谓临界速度的严格结果。更具体地说，我们证明了在 2 自由度哈密顿量 He e 的能级 0 中的异斜轨道被破坏，从而在指数级小（e）能级的某些元素（无穷远）之间产生异斜连接。在这种情况下，梅尔尼科夫理论不适用，因为存在指数级小的现象。