The objective of this paper is to extend some results of pioneers for the nonlinear equation mt=(1/2)(1/mk)xxx−(1/2)(1/mk)x introduced by Qiao. The equivalent relationship of the traveling wave solutions between the integrable equation and the generalized KdV equation is revealed. Moreover, when k=−(p/q)  (p≠q and p,q∈ℤ+), we obtain some explicit traveling wave solutions by the bifurcation method of dynamical systems.