[yor_on (OP)]

Keep it as simple as possible please.

As a example: https://physics.stackexchange.com/questions/285083/what-is-the-definition-of-soliton
And https://www.sciencedirect.com/science/article/abs/pii/0960077994900329
=

If you look at the second source they seem to mix into each other, and that's what I'm curios about.

[Jarek Duda]

Soliton is stable localized field configuration, according to https://en.wikipedia.org/wiki/Soliton

In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity.

I recommend sine-Gordon model: just phi_tt = pxi_xx - sin(psi), which can be realized with sequence of pendula, and has "particles" with pair creation/annihilation ... and practically entire special relativity: Lorentz contraction, time dilation, mass/momentum scaling.
https://en.wikipedia.org/wiki/Sine-Gordon_equation
"A Rubber Band Model Of the Universe":

Phonon is standing mechanical wave of lattice e.g. crystal ... which can be treated as real particle in perturbative QFT, in contrast to soliton it is rather not localized.

Exciton is something different, atom-like solid state dynamical situation e.g. in semiconductor: https://en.wikipedia.org/wiki/Exciton

An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force.

[Colin2B]

@yor_on I hadn’t come across excitons and phonons interactions creating solitons, but you might be interested in http://web.mit.edu/robertsilbey/research/papers/1964-1970/rsilbey_exciton-phonon_interactions_molecular_crystals.pdf

[evan_au]

Here is a recent application of solitons, as a way of producing many accurately-spaced optical wavelengths (an optical comb).

If it can be manufactured cheaply, it may provide a way to increase internet bandwidth, by assisting the transmission of data on many different wavelengths at once, in parallel.

See: https://spectrum.ieee.org/nanoclast/semiconductors/optoelectronics/micro-comb

[Jarek Duda]

Interestingly, topological solitons e.g. fluxon ( https://en.wikipedia.org/wiki/Fluxon ) observed in supercoductor undergo e.g.:
- interference: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.85.094503
- tunneling: https://journals.aps.org/prb/pdf/10.1103/PhysRevB.56.14677
- Aharonov-Bohm: http://www.tau.ac.il/~yakir/yahp/yh33

It brings a question what is the difference between such fluxon as "quant" of magnetic field, and e.g. electron as "quant" of electric charge?
Electron as electric charge is stable localized E~1/r^2 electric field configuration - isn't it a soliton?

[evan_au]

Electron as electric charge is stable localized E~1/r^2 electric field configuration - isn't it a soliton?

A soliton is a wave-type phenomena, where the aggregate behavior of many particles produces a net behavior which is the stable propagation of energy, without dispersion.
- It was originally described as a stable water wave propagating along a canal
- The aggregate behavior of many water molecules produces a net behavior which is the stable propagation of a water wave, without dispersion.

The difference with an electron is that it is a fundamental particle (as far as we know today). As a fundamental particle, it cannot dissipate by attenuation or dispersion.
- So I would not call it a soliton
- It is merely obeying Newton's laws of motion (with some Heisenberg uncertainty)

See: https://en.wikipedia.org/wiki/Soliton

[evan_au]

what is the difference between such fluxon as "quant" of magnetic field, and e.g. electron as "quant" of electric charge?

Flux pinning in Type II superconductors represents the aggregate behavior of many electrons
- Electron supercurrents swirl around magnetic lines of force, to neutralize the magnetic field in the body of the superconductor (Lenz's Law on steroids)
-But these magnetic swirls don't propagate across the superconductor - in fact, they tend to be pinned in place by the external magnetic field interacting with the superconductor. So I wouldn't call it a soliton.

An electron, as a fundamental particle, can propagate freely through a vacuum.

See: https://en.wikipedia.org/wiki/Flux_pinning

[Jarek Duda]

Solitons require a field - in superconductors it is effective field describing e.g. dynamics of electrons.
In vacuum we also have field(s) - corresponding to interactions, starting with electromagnetic - the question is if particles are solitons of some vacuum fields?
Electron is e.g. E~1/r^2 stable localized configuration of one of these vacuum fields: electric, doesn't it technically make it a soliton?

As a fundamental particle, it cannot dissipate by attenuation or dispersion.

Sure, isn't it also in definition of soliton?
To disperse energy of a particle, we need to annihilate it with antiparticle - exactly as for solitons, starting with sine-Gordon, which kinks "cannot dissipate by attenuation or dispersion".
Kink-antikink annihilation from https://en.wikipedia.org/wiki/Topological_defect :