Asymptotic profiles of solutions for the generalized Fornberg–Whitham equation with dissipation

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