Nonlocal Lie-Bäcklund Symmetries and Olver Symmetries of theKdV Equation

Starting from a special nonlocal Lie Bäcklund symmetry of the KdV, mKdV. Potential mKdV and singularity manifold equation system, three sets of higher order nonlocal Olver symmetries are reobtained. The soliton solutions of these models can also be obtained from the finite Lie- Bäcklund transformations.