Kinks in higher-order polynomial models

Abstract

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.

arXiv comment22 pages, 8 figures; final/published version

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• Connections between kinks with different asymptotics
• Exact BPS double-kinks in generalized ${\varphi }^4$, ${\varphi }^6$ and sine-Gordon models
• Wobbling kinks and shape mode interactions in a coupled two-component ${\varphi }^4$ theory
• Long-range interaction of kinks in higher-order polynomial models
• Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions
• Kink dynamics in a high-order field model
• Compact, long-range and vacuumless regimes controlled by scalar fields in two-dimensional flat and five-dimensional warped geometries