  In 1927 Louis de Broglie proposed an alternative approach to standard quantum
mechanics known as the double solution program (DSP) where particles are
represented as bunched fields or solitons guided by a base (weaker) wave. DSP
evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also
known as Bohmian mechanics but the general idea to use solitons guided by a
base wave to reproduce the dynamics of the PWI was abandonned. Here we propose
a nonlinear scalar field theory able to reproduce the PWI for the
Schr\"{o}dinger and Klein-Gordon guiding waves. Our model relies on a
relativistic `phase harmony' condition locking the phases of the solitonic
particle and the guiding wave. We also discuss an extension of the theory for
the $N$ particles cases in presence of entanglement and external (classical)
electromagnectic fields.
