  Starting from nonlocal symmetries related to B\"acklund transformation (BT),
many interesting results can be obtained. Taking the well known potential KdV
(pKdV) equation as an example, a new type of nonlocal symmetry in elegant and
compact form which comes from BT is presented and used to make researches in
the following three subjects: two sets of negative pKdV hierarchies and their
corresponding bilinear forms are constructed; the nonlocal symmetry is
localized by introduction of suitable and simple auxiliary dependent variables
to generate new solutions from old ones and to consider some novel group
invariant solutions; some other models both in finite dimensions and infinite
dimensions are generated by comprising the original BT and evolution under new
nonlocal symmetry. The finite-dimensional models are completely integrable in
Liouville sense, which are shown equivalent to the results given through the
nonlinearization method for Lax pair.
