Spectral stability for subsonic traveling pulses of the Boussinesq `abc' system

We consider the spectral stability of certain traveling wave solutions of the Boussinesq `abc' system. More precisely, we consider the explicit $sech^2(x)$ like solutions of the form $(\vp(x-w t), \psi(x- w t)=(\vp, const. \vp)$, exhibited by M. Chen (1998) and we provide a complete rigorous characterization of the spectral stability in all cases for which $a=c<0, b>0$.