New explicit solutions of the fifth-order KdV equation with variable coefficients

By means of the modified CK’s direct method, we give out the relationship between variable coefficients of the fifth-order KdV equation and the corresponding constant coefficient ones. At the same time, we have studied the generalized fifth-order KdV equation with constants coefficients using the Lie symmetry group methods. By applying the nonclassical symmetry method we found that the analyzed model does not admit supplementary, nonclassical type, symmetries. At last, we give some exact analytic solutions by using the power series method.