  The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited.
The equation is shown to permit solutions in the form of breathers
(nondispersive oscillating/spinning solitons), displaying simultaneous
particle-like and wave-like behavior adaptable to the properties of the de
Broglie clock. Within this formalism the de Broglie wave acquires the meaning
of a localized excitation of the classical action function. The problem of
quantization in terms of the breathing action function is discussed.
