We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model -- it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically $\phi^{14}$, $\phi^{16}$ and $\phi^{18}$.

中文翻译：

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具有超超指数扭结曲线和尾部的对数势

我们考虑了一种具有超超指数扭结曲线和扭结尾的对数势的新型一维模型。我们提供模型的解析扭结解决方案——它有 3 个扭结、3 个镜像扭结和相应的反扭结。虽然一些扭结尾巴是超超指数的，但其他一些是超指数的，而其余的则是指数的。线性稳定性分析表明，零模式和连续介质的开始之间存在间隙。最后，我们将这种势能及其扭结解与包含七个退化极小值的超高阶场论及其伴随的扭结解，特别是 $\phi^{14}$、$\phi^{16}$ 和 $\phi ^{18}$。