  This technical note is a complement to an earlier paper [Benzoni-Gavage \&
Rosini, Comput. Math. Appl. 2009], which aims at a deeper understanding of a
basic model for propagating phase boundaries that was proved to admit surface
waves [Benzoni-Gavage, Nonlinear Anal. 1998]. The amplitude equation governing
the evolution of weakly nonlinear surface waves for that model is computed
explicitly, and is eventually found to have enough symmetry properties for the
associated Cauchy problem to be locally well-posed.
