De Broglie-type relations from nonlinear evolution equations (Q1376503)

The localized solutions of certain nonlinear evolution equations, which can be presented in a complex Hamiltonian form, are well known to describe movement of some point-like particles under influence of external fields. The author has shown that the energy and momentum of such a type of solution are connected to the frequency and wave vector by de Broglie-type relations where the normalization constant of the solution appears instead of the Planck constant. In the paper this statement is proved for equations which are invariant under gauge type I transformations. The author discusses a possible relevance of these findings to the interpretation of quantum mechanics.