Kinks in higher-order polynomial models

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.

Automated summary

In this study, we investigate a family of field-theoretic models involving a real scalar field in (1+1)-dimensional space-time. The dynamics of the field in each model is determined by a polynomial potential with two degenerate minima. We derive exact general formulas for kink solutions exhibiting power-law asymptotic behavior. Additionally, we provide formulas for the asymptotics of all discovered kinks and analyze other properties such as stability potentials, zero modes, and positions of the centers of mass for the obtained kinks.