Scalar-field kink

A scalar-field kink is a one-dimensional finite-energy static solution approaching different vacua as $x\to -\infty$ and $x\to +\infty$. Its boundary values define a topological sector.

Kinks in a phi-six model commonly arise from a nonnegative degree-six potential with three degenerate vacua. For the unit-vacuum normalizationthe kink joining $0$ to $1$ isand has mass $1/4$. A rescaled model with $U(\varphi )={\varphi }^2({\varphi }^2-4{)}^2$ has the elementary kinkand its mass is $4\sqrt{2}$ in the normalization $E=\int [({\varphi }^{\prime }{)}^2/2+U]dx$.

If a proposed kink must cross a third degenerate vacuum, its first integral makes both the field derivative and potential vanish there. ODE uniqueness prevents it from crossing at finite distance, so the two elementary kink sectors can be joined only at infinite separation.