  We consider the Kawahara model and two fourth order semi-linear Schr\"odinger
equations in any spatial dimension. We construct the corresponding normalized
ground states, which we rigorously show to be spectrally stable.
  For the Kawahara model, our results provide a significant extension in
parameter space of the current rigorous results. At the same time, we verify
and clarify recent numerical simulations of the stability of these solitons.
For the fourth order NLS models, we improve upon recent results on stability of
very special, explicit solutions in the one dimensional case. Our
multidimensional results for fourth order NLS seem to be the first of its kind.
Of particular interest is a new paradigm that we discover herein. Namely, all
else being equal, the form of the second order derivatives (mixed second
derivatives vs. pure Laplacian) has implications on the range of existence and
stability of the normalized waves.
