  We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357)
equation on bounded one-dimensional domains. Under appropriate conditions
stripes with wave number $k\approx 1$ bifurcate supercritically from the zero
state and form S-shaped branches resulting in bistability between small and
large amplitude stripes. Within this bistability range we find stationary
heteroclinic connections or fronts between small and large amplitude stripes,
and demonstrate that the associated spatially localized defect-like structures
either snake or fall on isolas. In other parameter regimes we also find
heteroclinic connections to spatially homogeneous states, and a multitude of
dynamically stable steady states consisting of patches of small and large
amplitude stripes with different wave numbers or of spatially homogeneous
patches. The SH357 equation is thus extremely rich in the types of patterns it
exhibits. Some of the features of the bifurcation diagrams obtained
  by numerical continuation can be understood using a conserved quantity, the
spatial Hamiltonian of the system.
