标题： 标量场模型中多项式相互作用的解析短程和长程扭结-like结构 显示英文标题

标题： Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions

摘要： 我们研究了一类标量场模型，在多项式势的存在下，这些模型会产生类似孤子的解，这些势允许修改局域构型的尾部。 我们在势中引入一个参数来控制与极小值相关的经典质量。 通过使用Bogomol'nyi发展的第一阶框架，我们得到了解析解，随着该参数的增加，这些解变得越来越相互作用。 通过研究该参数趋于无穷大的极限情况，孤子解呈现出幂律尾部，我们展示了这一特征与经典质量的行为有关，后者在上述极限情况下消失。 我们还研究了对微小扰动的稳定性，结果显示，根据参数值的不同，稳定性势可能支持多个束缚态，也可能呈现火山状轮廓。 显示英文摘要

摘要： We investigate a class of scalar field models which engender kink-like solutions in the presence of polynomial potentials that allows for modifications of the tails of the localized configurations. We introduce a parameter in the potential that controls the classical mass associated to its minima. By using the first-order framework developed by Bogomol'nyi, we obtain analytical solutions that become more and more interactive as we increase such parameter. By investigating the limit in which the parameter tends to infinite, the kink solution gets power law tails, and we show that this feature is related to the behavior of the classical mass, which vanishes in the aforementioned limit. We also investigate the stability against small fluctuations, with the results unveiling that, depending on the values of the parameter, the stability potential may support several bound states and also, it may attain a volcano-like profile.