  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.
