  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.
