  Various dualities are summarized. Based on the universal wave-particle
duality, along an opposite direction of the developed quantum mechanics, we use
a method where the wave quantities frequency and wave length are replaced on
various mechanical equations, and may be derive some new results. It is called
the mechanical wave theory. From this we derive new operators which represent
more physical quantities. Further, we propose some nonlinear equations and
their solutions, which may be probably applied to quantum theory.
