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There were many physicists suggesting such approaches in the history, like seeing particle as kind of a vortex. The most popular model is probably of Tony Skyrme ( http://en.wikipedia.org/wiki/Skyrmion ), seeing mesons/baryons as topological solitons of some effective field.

There are well known Abrikosov vortices/fluxons - topological solitons in superconductor. We can observe them through a microscope, but it doesn't prevent "quantum" phenomenas for them, like interference ( http://prl.aps.org/abstract/PRL/v71/i14/p2311_1 ).

Recent Couder's droplets are different complex macroscopic objects with quantum properties (thread: https://www.physicsforums.com/showthread.php?t=550729 ) - localized objects conjugated with waves they create, what leads to observed:

- interference in double-slit experiment (particle goes a single way, but "pilot" waves it creates go through all paths - leading to interference): http://prl.aps.org/abstract/PRL/v97/i15/e154101 ,

- tunneling (the field depends on the whole history, making that getting through a barrier is practically random): http://prl.aps.org/abstract/PRL/v102/i24/e240401 ,

- orbit quantization (to find a resonance with the field, the clock has to perform an integer number of periods while enclosing an orbit): http://www.pnas.org/content/107/41/17515 ,

- "classical Zeeman effect" (Coriolis force instead of Lorentz): http://prl.aps.org/abstract/PRL/v108/i26/e264503.

So there is a localized configuration - corpuscle (e.g. charge), conjugated with waves it creates - because of some internal periodic dynamics (so called de Broglie's clock, zitterbewegung).

In the language of fields: localized configuration is a soliton, conservation laws with integer "quantum" numbers naturally appears while using topological solitons (e.g. with topological charge), which often have some internal periodic dynamics, like breathers ( http://en.wikipedia.org/wiki/Breather ).

Prof. Faber has shown that in a field of just unit vectors, defining electric/magnetic field through curvature of the field, the dynamics of topological solitons (hedgehog configurations) is given by Maxwell equations - we get a simple electron model (massive) with standard electrodynamics: http://iopscience.iop.org/1742-6596/361/1/012022/ http://arxiv.org/abs/hep-th/9910221.

Here is my essay with more motivations for using soliton particle models and expansion of Faber's model by a single degree of freedom ("quantum phase"), making that the family of topological solitons grows to resemble our particle menagerie with their dynamics: http://www.fqxi.org/data/essay-contest-files/Duda_elfld_1.pdf.

What do you generally think about this kind of approaches?

Are solitons only some abstract mathematical constructs?

Maybe there are also macroscopic solitons like fluxons?

Maybe we can use solitons also for effective models of particles like Skyrme?

... or maybe all particles are just solitons of some fundamental field? What field?