The Kakutani Kawahara equation ut+uux+buxxx-a(ut+uux)x=0(b>0,a≥0)was considered.By using the theory of planar dynamical systems, its bounded traveling wave solutions was analysed to obtain the conditions for their existence. In dispersion dominant case,it was found that the unique bounded traveling wave solution of the equation is of oscillatory and damped property. Furthermore,according to the evolution of orbits in the global phase portraits, an approximate damped oscillatory solution for this equation was presented by using the undetermined coefficients method. Finally,in accordance with the idea of homogenization principle,an integral equation which reflects the relation between the approximate solution and the exact damped oscillatory solution was provided and thereby the errorestimate was achieved. The error is an infinitesimal speedyly decreasing in exponential form.