标题： 标量场模型中高阶自相互作用的孤子散射 显示英文标题

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

摘要： 二维中的高阶纯量场模型，包括$\phi^8$模型，已经被研究过。研究表明，对于势的某些特殊位置的极小值，可以找到显式的孤立子解。然而，在物理应用中，知道一个模型对于任意极小值位置的所有显式解是非常重要的。在目前的研究中，借助一些变形函数，我们展示了可以通过显式孤立子获得高阶纯量场理论。特别是，我们引入了两个变形函数，当它们应用于著名的$\phi^4$和$\phi^6$模型时，分别生成修改后的$\phi^8$和$\phi^{10}$模型，这些模型的所有显式孤立子解都依赖于一个单一参数。由于这个参数控制着势的极小值的位置，我们在许多不同的情况下发现了有趣的新的解。我们也研究了这两个新修改模型的孤立子质量、激发光谱的行为以及多个孤立子-反孤立子碰撞。碰撞结果由初始构型决定，具体来说是由孤立子-反孤立子和反孤立子-孤立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，这可能可以通过模型中存在的一组内部模式来解释。 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.