Explicit kinks in higher-order field theories

Abstract

We study an example of higher-order field-theoretic model with an eighth-degree polynomial potential -- the ${\phi }^8$ model. We show that for some certain ratios of constants of the potential, the problem of finding kink-type solutions in $(1+1)$-dimensional space-time reduces to solving algebraic equations. For two different ratios of the constants, which determine positions of the vacua, we obtained explicit formulas for kinks in all topological sectors. The properties of the obtained kinks are also studied -- their masses are calculated, and the excitation spectra which could be responsible for the appearance of resonance phenomena in kink-antikink scattering are found.

25 pages, 7 figures; v2: major revision; matches the published version

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Cited by in corpus (18)

• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink-antikink collisions in the ${\varphi }^8$ model: short-range to long-range journey
• Deformations of Kink Tails
• Kinks in higher-order polynomial models
• Exotic Final States in the ${\phi }^8$ Multi-Kink Collisions
• Kink solutions in logarithmic scalar field theory: Excitation spectra, scattering, and decay of bions
• Collision of ${\varphi }^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness
• Scattering of kinks in the $B{\phi }^4$ model
• Collisions between kinks with long-range tails: a simple and efficient method
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons
• Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models
• Kink Collision in the Noncanonical ${\phi }^6$ Model: A Model with Localized Inner Structures
• Domain wall thickness and deformations of the field model
• Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions
• From thin to thick domain walls: An example of the ${\phi }^8$ model
• Scattering of kinks in scalar-field models with higher-order self-interactions
• Kink dynamics in a high-order field model
• Kinks scattering in deformed ${\phi }^6$ model