Solitons in a class of interacting scalar field theories without $SO(2)$ invariance

Abstract

In this article, we study kink soliton configurations in interacting scalar field theories containing two fields without $SO(2)$ invariance. We study a class of such theories, the well-known Montonen-Sarker-Trullinger-Bishop model is one of them. These models are interesting since the $U(1)$ current is not conserved in them due to the presence of explicit symmetry breaking terms in the action. The existence of kink soliton configurations is shown in terms of a system of first-order ordinary differential equations. Although $U(1)$ current in these models are non-conserved, our approach is general enough to study soliton configurations in a generic two interacting scalar field theory. We also discuss other benefits of this approach.