Sine-Gordon kink lattice

TL;DR

This paper introduces a coupled scalar field model combining sine-Gordon and $\chi^4$ potentials, deriving BPS solutions including a kink lattice, and analyzes their stability and how interaction strength influences the lattice structure.

Contribution

It presents a novel coupled scalar field model with sine-Gordon and $\chi^4$ potentials, deriving BPS solutions and analyzing the formation and stability of kink lattices.

Findings

Single kink-kink configuration identified.

Inhomogeneous sine-Gordon kink lattice constructed.

Homogeneous lattice emerges under strong interactions.

Abstract

We consider an extended model with two real scalar fields, $\phi(x,t)$ and $\chi(x,t)$. The first sector is controlled by the sine-Gordon superpotential, while the second field is submitted to the $\chi^4$ one. The fields mutually interact via a nontrivial coupling function $f(\chi)$ that also changes the kinematics of $\phi$. We briefly review the implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) prescription. We then solve the resulting BPS equations for two different interactions $f$. The first one leads to a single kink-kink configuration, while the second one gives rise to a inhomogeneous sine-Gordon kink lattice. We study the linear stability of these new solutions, focusing on their translational modes. We also explore how the strength of the mutual interaction affects the BPS profiles. In particular, we show that a homogeneous lattice with identical kinks is attained in the regime of extremely strong interactions.