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We consider the (1+1)-dimensional Lorentz-symmetric field-theoretic modelwith logarithmic potential having a Mexican-hat form with two local minimasimilar to that of the quartic Higgs potential in conventional electroweaktheory with spontaneous symmetry breaking and mass generation. We demonstratethat this model allows topological solutions -- kinks. We analyze the kinkexcitation spectrum, and show that it does not contain any vibrational modes.We also study the scattering dynamics of kinks for a wide range of initialvelocities. The critical value of the initial velocity occurs in kink-antikinkcollisions, which thus differentiates two regimes. Below this value, we observethe capture of kinks and their fast annihilation; while above this value, thekinks bounce off and escape to spatial infinities. Numerical studies show noresonance phenomena in the kink-antikink scattering.

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