Limit speed of traveling wave solutions for the perturbed generalized KdV equation

The existence of solitary waves and periodic waves for a perturbed generalized KdV equation is established by using geometric singular perturbation theory. It is proven that the limit wave speed $ c_{0}(h) $ is decreasing by analyzing the ratio of Abelian integrals for $ n = 2 $ and $ n = 3 $. The upper and lower bounds of the limit wave speed are given. Moreover, the relation between the wave speed and the wavelength of traveling waves is obtained. Our results answer partially an open question proposed by Yan, Liu and Liang [Math. Model. Anal., 19 (2014), pp. 537-555].