  We present a new class of exact fireball solutions of relativistic
dissipative hydrodynamics. We describe new exact solutions both for the
relativistic Navier-Stokes and for the Israel-Stewart theory, for arbitrary
shear and bulk viscosities, as well as for other dissipative coefficients. The
common property of these solutions is the presence of the relativistic Hubble
flow. Our results generalize the recently found first solution in these
classes, for an arbitrary temperature dependent speed of sound, shear and bulk
viscosity, heat conduction and fluctuating initial temperature profiles. These
solutions are causal and not only stable but also asymptotically perfect. A
strong and narrow peak in the kinematic bulk viscosity is shown to imitate the
effects of a first order phase transition. The new class of asymptotically
perfect solutions is thus found to be very rich, but at the same time mostly
academic as the solutions are limited by the spherical symmetry of the Hubble
flow field.
