= Kink in a phi-six model
{title2=$\phi^6$ kink}
Kinks in a phi-six model commonly arise from a nonnegative degree-six potential with three degenerate vacua. For the unit-vacuum normalization
$$
U(\phi)=\frac12\phi^2(1-\phi^2)^2,
$$
the kink joining $0$ to $1$ is
$$
\phi(x)=\frac1{\sqrt{1+e^{-2(x-x_0)}}}
$$
and has mass $1/4$. A rescaled model with $U(\phi)=\phi^2(\phi^2-4)^2$ has the elementary kink
$$
\phi(x)=\frac2{\sqrt{1+e^{-8\sqrt2(x-x_0)}}},
$$
and its mass is $4\sqrt2$ in the normalization $E=\int[(\phi')^2/2+U]dx$.
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