标题： 标量场模型中孤子的散射行为 显示英文标题

标题： Scattering of kinks in scalar-field models with higher-order self-interactions

摘要： 高维标量场模型在二维中，包括$\phi^8$模型，已经进行了研究。 已经证明，对于势能极小位置的一些特殊情况，可以找到显式的孤子解。 然而，在物理应用中，了解模型在任何极小位置的所有显式解是非常重要的。 在本研究中，借助一些变形函数，我们表明可以通过显式孤子得到高阶标量场理论。 特别是，我们引入了两个变形函数，当应用于著名的$\phi^4$和$\phi^6$模型时，分别产生修改后的$\phi^8$和$\phi^{10}$模型，这些模型具有所有依赖于单个参数的显式类孤子解。 由于这个参数控制势能极小值的位置，我们在许多不同的情况下找到了有趣的新解。 我们还研究了孤子质量、激发谱的行为以及这两个新修改模型的多个孤子-反孤子碰撞。 碰撞结果由初始配置决定，具体来说是由孤子-反孤子和反孤子-孤子配对出现的顺序决定的。 另一个有趣的发现是共振窗口的抑制，这可能由模型中一组内部模式的存在来解释。 显示英文摘要

摘要： Higher-order scalar field models in two dimensions, including the $\phi^8$ model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found. However, in physical applications, it is very important to know all the explicit solutions of a model for any minima position. In the present study, with the help of some deformation functions, we have shown that higher-order scalar field theories can be obtained with explicit kinks. In particular, we introduced two deformation functions that, when applied to the well known $\phi^4$ and $\phi^6$ models, produce modified $\phi^8$ and $\phi^{10}$ models, respectively, with all their explicit kink-like solutions which depend on a single parameter. Since this parameter controls the position of the minima of the potential, we have found interesting new solutions in many distinct cases. We have also studied the kink mass, the behavior of the excitation spectra and several kink-antikink collisions for these two new modified models. The collision outcome is determined by the initial configuration, specifically the sequence in which the kink-antikink and antikink-kink pairings emerge. Another interesting finding is the suppression of resonance windows, which may be explained by the presence of a set of internal modes in the model.