  We consider a family of field-theoretic models with a real scalar field in
(1+1)-dimensional space-time. The field dynamics in each model is determined by
a polynomial potential with two degenerate minima. We obtain exact general
formulas for kink solutions with power-law asymptotic behavior. We also write
out formulas for the asymptotics of all found kinks. In addition, we analyze
some other properties of the obtained kinks: stability potentials, zero modes,
positions of the centers of mass.
