The de Broglie Wave as a Localized Excitation of the Action Function

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.