= Sine-Gordon breather spectrum at reflectionless couplings
{c}
{title2=$m_k=2M\sin[k\pi/(2n)],\quad k=1,\ldots,n-1$}
At renormalized coupling $\gamma=8\pi/n$, the kink-antikink transmission <poles> lie at $\vartheta=i\pi(1-k/n)$. The <relativistic bound-state mass from a rapidity pole> gives the displayed increasing <breather> <masses>. The <kink> <mass> is $M=mn/\pi$, and $k=n$ is an excluded threshold state. No <breathers> occur at $n=1$; scattering involving a physical second <breather> requires $n\geq3$.
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