Logarithmic Potential with Super-Super-Exponential Kink Profiles and Tails

Abstract

We consider a novel one dimensional model of a logarithmic potential which has super-super-exponential kink profiles as well as kink tails. We provide analytic kink solutions of the model -- it has 3 kinks, 3 mirror kinks and the corresponding antikinks. While some of the kink tails are super-super-exponential, some others are super-exponential whereas the remaining ones are exponential. The linear stability analysis reveals that there is a gap between the zero mode and the onset of continuum. Finally, we compare this potential and its kink solutions with those of very high order field theories harboring seven degenerate minima and their attendant kink solutions, specifically ${\varphi }^{14}$, ${\varphi }^{16}$ and ${\varphi }^{18}$.

23 pages, 14 figures

References in corpus (4)

• Kink-kink and kink-antikink interactions with long-range tails
• Long-range interactions of kinks
• Highly interactive kink solutions
• Topological defects with power-law tails

Cited by in corpus (7)

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• Explicit Kink Solutions in Several One-Parameter Family of Higher Order Field Theory Models
• Superposed Hyperbolic Kink and Pulse Solutions of Coupled ${\varphi }^4$, NLS and MKdV Equations
• Novel Deformation Function Creating or Destroying any Number of Even Kink Solutions
• Compact structures in impurity-doped vacuumless systems
• Kink dynamics in a high-order field model
• Remarks on sine-Gordon kink--fermion system: localized modes and scattering