  Compactons are compactly supported solitary waves for nondissipative
evolution equations with nonlinear dispersion. In applications, these model
equations are accompanied by dissipative terms which can be treated as small
perturbations. We apply the method of adiabatic perturbations to compactons
governed by the K(n,n) Rosenau-Hyman equation in the presence of dissipative
terms preserving the "mass" of the compactons. The evolution equations for both
the velocity and the amplitude of the compactons are determined for some linear
and nonlinear dissipative terms: second-, fourth-, and sixth-order in the
former case, and second- and fourth-order in the latter one. The numerical
validation of the method is presented for a fourth-order, linear, dissipative
perturbation which corresponds to a singular perturbation term.
