  We study different forms of linear and non-linear field equations, so-called
`phase-field' equations, in relation to the de~Broglie-Bohm double solution
program. This defines a framework in which elementary particles are described
by localized non-linear wave solutions moving by the guidance of a pilot wave,
defined by the solution of a Schr\"odinger type equation. First, we consider
the phase-field order parameter as the phase for the linear pilot wave, second
as the pilot wave itself and third as a moving soliton interpreted as a massive
particle. In the last case, we introduce the equation for a superwave, the
amplitude of which can be considered as a particle moving in accordance to the
de~Broglie-Bohm theory. Lax pairs for the coupled problems are constructed in
order to discover possible non-linear equations which can describe the moving
particle and to propose a framework for investigating coupled solutions.
Finally, doublons in 1+1 dimensions are constructed as self similar solutions
of a non-linear phase-field equation forming a finite space-object. Vacuum
quantum oscillations within the doublon determine the evolution of the coupled
system. Applying a conservation constraint and using general symmetry
considerations, the doublons are arranged as a network in 1+1+2 dimensions
where nodes are interpreted as elementary particles. A canonical procedure is
proposed to treat charge and electromagnetic exchange.
