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We add a theorem to [J. Differential Equations 257 (2014), no. 3, 720--758]by F. Achleitner, C.M. Cuesta and S. Hittmeir. In that paper we studiedtravelling wave solutions of a Korteweg-de Vries-Burgers type equation with anon-local diffusion term. In particular, the proof of existence and uniquenessof these waves relies on the assumption that the exponentially decayingfunctions are the only bounded solutions of the linearised equation. In thisaddendum we prove this assumption and thus close the existence and uniquenessproof of travelling wave solutions.

Addendum to "Travelling waves for a non-local Korteweg-de Vries-Burgers equation" [J. Differential Equations 257 (2014), no. 3, 720--758]