Questions tagged [solitons]
Solitons are self-stabilizing solitary wave packets maintaining their shape propagating at a constant velocity. They are caused by a balance of nonlinear and dispersive (where the speed of the waves varies with frequency) effects in the medium.
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Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
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Soliton and Goldstone boson
I'm learning Gross-Pitaevskii model. By spontaneous symmetry breaking one obtains Bogoljubov modes, which ensures Landau criterion. So those modes have two features, for one they are Goldstone bosons ...
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How to derive the ODE from the EOM of vortex?
In the Lagrangian mode we have the equation of motion
\begin{align}
\partial_\mu F^{\mu\nu}&=j^\nu. \\
D_{\mu }D^{\mu}\phi +\mu^{2}\phi-\lambda(\phi^{*}\phi)\phi &=0.
\end{align}
Since we ...
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Obtaining the topological charge
I want to obtain the topological charge or winding number of the map
$$
f_n(\mathbf{r})=(\sin \theta \cos (n \varphi), \sin \theta \sin (n \varphi), \cos \theta)
$$
and my lecture notes say that it is ...
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Soliton in non-degenerate polymer
I just started reading about the conduction mechanism in polymer. From what i read, polarons are used as method of charge transportation in non-degenerate polymer. While for degenerate polymer, both ...
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Why do soliton modes in polyacetylene have to appear at the edges of an open boundary chain?
When calculating the presence of soliton or anti-soliton in the extreme dimerization polyacetylene SSH model, we say that in the case of open-boundary condition and odd number of atoms, we must have ...
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What is the topology of sine-Gordon equation?
In one pdf on solitons, I am finding the following written
For the sine-Gordon theory, it is much better to think of $\phi$ as a field modulo $2\pi$, i.e. as a function $\phi: R \rightarrow S_{1}$. ...
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Do topological solitons allow modeling non-degenerate multiple vacua?
I am not well-versed in the research on topological solitons but am interested to make a good sense of its implication.
The highly interesting point in this new talk by Nick Manton was where he is ...
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Overview work on radio solitons?
I've heard about solitons in dense mediums (water), sparse mediums (acoustic) and optical fiber.
But I can't find a good overview work on solitons in radio spectrum. Something like generating EM ...
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Why only $\phi=\pm1$ are considered "vacuum states" in the Klein-Gordon model with $\phi^4$ potential, and not $\phi=0$?
I am reading "Kink Moduli Spaces — Collective Coordinates Reconsidered," by Manton, Oleś, Romańczukiewicz, and Wereszczyński (arXiv version), where they consider the Klein-Gordon equation,
$$...
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Scale transformation of the scalar field and gauge field
I am reading this paper: "Magnetic monopoles in gauge field theories", by Goddard and Olive. I don't understand some scale transformations that appear in Page 1427.
Start from the energy ...
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Can a "depressive soliton" wave exist? That is, can we have a trough without any crest? Why or why not?
I know that "soliton" waves can consist of a crest without a trough. One would expect the reverse to be true as well.
However, this Wikipedia excerpt says,
So for this nonlinear gravity ...
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Formation of optical solitons in microresonators
Optical soliton formation in laser systems with devices that facilitate mode-locking such as a saturable absorber help me understand why solitons form in the first place.
However, when one considers a ...
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Arbitrary heat kernel coefficients of covariant Laplacian with instanton
The heat kernel coefficients $b_{2k}(x,y)$ of the covariant Laplacian in an $SU(2)$ instanton background (for simplicity let's say $q=1$ topological charge, so the 't Hooft solution) on $R^4$ is ...
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Sine-gordon mass term
Simple question: are there some notes or explicit calculations of the mass term from the paper of Zamolodchikov - Mass scale in the sine-gordon model and its reduction (1994)? I need to justify this ...
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