  The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited.
The equation is shown to permit solutions in the form of breathers
(oscillating/spinning solitons), displaying simultaneous particle-like and
wave-like behavior. The de Broglie wave thus acquires a clear deterministic
meaning of a wave-like excitation of the classical action function. The problem
of quantization in terms of the breathing action function and the double-slit
experiment are discussed.
