Kink solutions in a generalized scalar $\phi^4_G$ field model

Abstract

We study a scalar field model in a two dimensional space-time with a generalized $\phi^4_G$ potential which has four minima, obtaining novel kink solutions with well defined properties although the potential is non-analytical at the origin. The model contains a control parameter $\delta$ that breaks the degeneracy of the potential minima, giving rise to two different phases for the system. The $\delta<0$ phases do not possess solitary wave solutions. At the transition point $\delta=0$ all the potential minima are degenerate and three different kink solutions result. As the transition to the $\delta>0$ phase takes place, the minima of the potential are no longer degenerate and a unique kink $\phi_\delta$ solution is produced. Remarkably, this kink is a coherent structure that results from the merge of three kinks that can be identified with those observed at the transition point. To support the interpretation of $\phi_\delta$ as a bound state of three kinks, we calculate the force between the kink-kink pair components of $\phi_\delta$, obtaining an expression that has both exponentially repulsive and constant attractive contributions that yields an equilibrium configuration, explaining the formation of the $\phi_\delta$ multi-kink state. We further investigate kink properties including their stability guaranteed by the positive defined spectrum of small fluctuations around the kink configurations. The findings of our work together with a semiclassical WKB quantization, including the one loop mass renormalization, enable computing quantum corrections to the kink masses. The general results could be relevant to the development of effective theories for non-equilibrium steady states and for the understanding of the formation of coherent structures.