Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 344 / 1 / b

For constant $\kappa$ and a planar profile,Far inside either bulk phase, derivatives vanish and $\varphi =\pm {\varphi }_B$, where ${\varphi }_B^2=-a/b$. ThereforeSince part a makes $\mu$ constant, it vanishes throughout the interface.