This result is sharp in the case where a = c, since for a, c bigger, some abed linear waves of nonzero frequency do have zero group velocity. Second, we sharply enlarge the interval of decay to consider the whole light cone, that is to say, any interval of the form vertical bar x vertical bar similar to vertical bar v vertical bar t for any vertical bar v vertical bar < 1. This result rules out, among other things, the existence of nonzero speed solitary waves in the regime where decay is present. Finally, we prove decay to zero of small abed solutions in exterior regions vertical bar x vertical bar >> vertical bar t vertical bar also discarding super-luminical small solitary waves. These three results are obtained by performing new improved virial estimates for which better decay properties are deduced.