In many books the $\phi^4$ model can produce a topological soliton called kink. Are they right? In the case of sine-Gordon model you can have a topological soliton due to you can express the Lagrangian in terms of two scalar fields taking values in a circle. As the field is constrained on a manifold the model could have stability. I am not sure if $\phi^4$ model could be viewed as a field constrained on a manifold also.
So my questions are:
Is it right to talk about topological solitons or kinks in $\phi^4$ model?
Has the $\phi^4$ model an alternative formulation as a constrained field with target space a circle or any other manifold?