  We consider the Cauchy problem for the generalized Fornberg-Whitham equation
with dissipation. This is one of the nonlinear, nonlocal and
dispersive-dissipative equations. The main topic of this paper is an asymptotic
analysis for the solutions to this problem. We prove that the solution to this
problem converges to the modified heat kernel. Moreover, we construct the
second term of asymptotics for the solutions depending on the degree of the
nonlinearity. In view of those second asymptotic profiles, we investigate the
effects of the dispersion, dissipation and nonlinear terms on the asymptotic
behavior of the solutions.
