  We show that there exists a duality family of self-interacting massive scalar
fields. The scalar field in a duality family are related by a duality
transformation. Such a duality of scalar fields is a field version of the
Newton-Hooke duality in classical mechanics. The duality transformation
preserves the type of the field equation: transforming a Klein-Gordon type
equation to another Klein-Gordon type equation with a different
self-interacting potential. Once a field in a duality family is solved, all
other family members are solved by the transformation. That is, a series of
exactly solvable models can be constructed from one exactly solvable model. The
dual field of the power-interaction field, the sine-Gordon field, etc., are
considered. Moreover, as a comparison, we show an analogue of the duality in
classical and quantum mechanics.

General Physics