  It is revealed that there exist duality families of the KdV type equation. A
duality family consists of an infinite number of generalized KdV (GKdV)
equations. A duality transformation relates the GKdV equations in a duality
family. Once a family member is solved, the duality transformation presents the
solutions of all other family members. We show some dualities as examples, such
as the soliton solution-soliton solution duality and the periodic
solution-soliton solution duality.
