  We study the properties of a relativistic model with logarithmic
nonlinearity. We show that such model allows two types of solutions:
topologically trivial (gaussons) and topologically non-trivial (kinks),
depending on a sign of the nonlinear coupling. We focus primarily on the kinks'
case and study their scattering properties. For the kink-antikink scattering,
we have found a critical value of the initial velocity, which separates two
different scenarios of scattering. For the initial velocities below this
critical value, the kinks form a bound state, which then decays slowly. If the
initial velocities are above the critical value, the kinks collide, bounce and
eventually escape to infinities. During this process, the higher initial
velocity is, the greater is the elasticity of the collision. We also study
excitation spectrum of the kink solution.
