Scattering of kinks in scalar-field models with higher-order self-interactions

Abstract

Higher-order scalar field models in two dimensions, including the ${\varphi }^8$ model, have been researched. It has been shown that for some special cases of the minima positions of the potential, the explicit kink solutions can be found. However, in physical applications, it is very important to know all the explicit solutions of a model for any minima position. In the present study, with the help of some deformation functions, we have shown that higher-order scalar field theories can be obtained with explicit kinks. In particular, we introduced two deformation functions that, when applied to the well known ${\varphi }^4$ and ${\varphi }^6$ models, produce modified ${\varphi }^8$ and ${\varphi }^{10}$ models, respectively, with all their explicit kink-like solutions which depend on a single parameter. Since this parameter controls the position of the minima of the potential, we have found interesting new solutions in many distinct cases. We have also studied the kink mass, the behavior of the excitation spectra and several kink-antikink collisions for these two new modified models. The collision outcome is determined by the initial configuration, specifically the sequence in which the kink-antikink and antikink-kink pairings emerge. Another interesting finding is the suppression of resonance windows, which may be explained by the presence of a set of internal modes in the model.

Version accepted for publication

References in corpus (22)

• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Spectral Walls in Soliton Collisions
• Deformed defects for scalar fields with polynomial interactions
• Kink Dynamics in a Parametric ${\varphi }^6$ System: A Model With Controllably Many Internal Modes
• Could the primordial radiation be responsible for vanishing of topological defects?
• Quintessential Inflation in a thawing realization
• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• Spectral walls in multifield kink dynamics
• Vacuum Polarization Energy for General Backgrounds in One Space Dimension
• Wobbling double sine-Gordon kinks
• 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
• Fermionic spectral walls in kink collisions
• Emerging Translational Variance: Vacuum Polarization Energy of the ${\varphi }^6$ kink
• Kink-antikink scattering in a quantum vacuum
• Resonance structures in kink-antikink scattering in a quantum vacuum
• Spectral walls in antikink-kink scattering in the ${\varphi }^6$ model
• Fermions on wobbling kinks: normal versus quasinormal modes
• 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
• Phonons scattering off discrete asymmetric solitons in the absence of a Peierls-Nabarro potential
• Dynamics of kink train solutions in deformed Multiple sine-Gordon models

Cited by in corpus (2)

• Kinks in generalized scalar field models and their scattering properties
• Analytical short- and long-range kink-like structures in scalar field models with polynomial interactions