  Recent asymptotic results by the authors provided detailed information on the
shape of solitary high-energy travelling waves in FPU atomic chains. In this
note we use and extend the methods to understand the linearisation of the
travelling wave equation. We show that there are not any other zero eigenvalues
than those created by the translation symmetry and this implies a local
uniqueness result. The key argument in our asymptotic analysis is to replace
the linear advance-delay-differential equation for the eigenfunctions by an
approximate ODE.
