We consider the $(1+1)$-dimensional Lorentz-symmetric field-theoretic model with logarithmic potential having a Mexican-hat form with two local minima similar to that of the quartic Higgs potential in conventional electroweak theory with spontaneous symmetry breaking and mass generation. We demonstrate that this model allows topological solutions — kinks. We analyze the kink excitation spectrum, and show that it does not contain any vibrational modes. We also study the scattering dynamics of kinks for a wide range of initial velocities. The critical value of the initial velocity occurs in kink-antikink collisions, which thus differentiates two regimes. Below this value, we observe the capture of kinks and their fast annihilation; while above this value, the kinks bounce off and escape to spatial infinities. Numerical studies show no resonance phenomena in the kink-antikink scattering.

我们认为 $(1+1)$维洛伦兹对称场论模型，具有墨西哥帽形式的对数势，具有两个局部最小值，类似于传统电弱理论中的四次希格斯势，具有自发对称性破坏和质量生成。我们证明了这个模型允许拓扑解决方案——扭结。我们分析了扭结激发光谱，并表明它不包含任何振动模式。我们还研究了各种初始速度下扭结的散射动力学。初始速度的临界值出现在扭结-反扭结碰撞中，因此区分了两种状态。低于这个值，我们观察到扭结的捕获和它们的快速湮灭；当高于此值时，扭结会反弹并逃逸到空间无穷大。