  We consider the asymptotic behavior of the global solutions to the initial
value problem for the generalized KdV-Burgers equation. It is known that the
solution to this problem converges to a self-similar solution to the Burgers
equation called a nonlinear diffusion wave. In this paper, we derive the
optimal asymptotic rate to the nonlinear diffusion wave when the initial data
decays slowly at spatial infinity. In particular, we investigate that how the
change of the decay rate of the initial value affects the asymptotic rate to
the nonlinear diffusion wave.
