Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 313 / 1 / i / Solution

The potential is even, so field reflection has $\alpha =-1$; spatial reflection has $\beta =-1$. If $K(x)={\varphi }^{(0,1)}(x)$, the four oriented interpolating solutions, allowing a common translation, areThe first and third are kinks under this orientation convention, and spatial reflection gives their antikinks.