Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions

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.