  The Robinson-Trautman type N solutions, which describe expanding
gravitational waves, are investigated for all possible values of the
cosmological constant Lambda and the curvature parameter epsilon. The wave
surfaces are always (hemi-)spherical, with successive surfaces displaced in a
way which depends on epsilon. Explicit sandwich waves of this class are studied
in Minkowski, de Sitter or anti-de Sitter backgrounds. A particular family of
such solutions which can be used to represent snapping or decaying cosmic
strings is considered in detail, and its singularity and global structure is
presented.
