  We consider the initial value problem associated to a large class of fifth
order nonlinear dispersive equations. This class includes several models
arising in the study of different physical phenomena. Our aim is to establish
special (space) decay properties of solutions to these systems. These
properties complement previous unique continuation results and in some case,
show that they are optimal. These decay estimates reflect the "parabolic
character" of these dispersive models in exponential weighted spaces. This
principle was first obtained by T. Kato in solutions of the KdV equation
