Let $I:=[0,L]$ and $\langle N\rangle$ be the average number each of kinks and antikinks (i.e. there are in average $N$ kinks and $N$ antikinks) in $I$. Moreover, let $\langle n\rangle=\frac{\langle N\rangle}{L}$ and $\frac{\langle m\rangle}{L}$, where $m$ is the kink density per unit length and $n$ is the antikink density per unit length.
The velocity of kink and antikink is given as $u$ and $-u$, respectively.
Now, let $\theta(x,t)$ be the displacement angle for $x\in I$ at time $t$.
Moreover, assume that each kink and antikink passing some fixed point $x$ along $I$ brings an increase of $2\pi$ in $\theta(x)$.
Therefore, I read, $$ \langle\partial\theta / \partial t\rangle=2\pi u (\langle n\rangle + \langle m\rangle ).~~~(*) $$
I have some problems to understand $(*)$. I guess that $u\langle n\rangle + u\langle m\rangle$ is the (average) number of kinks and antikinks per unit length that pass the fixed point $x$.
But how does this fit together with the units?
$\langle\partial\theta / \partial t\rangle$ should be something like the average angular velocity.
The velocity of the kinks and antikinks, $u$, hould be something like $$ u=\frac{\Delta z}{\Delta t} $$ where $\Delta z$ is some distance on $[0,L]$ and $\Delta t$ is some small time interval.
$\langle n\rangle$ and $\langle m\rangle$ are the average number of kinks and antikinks per uni length.
But I do not see why the right hand side of $(*)$ should give the average angular velocity.