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