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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Time dependent mass terms in field theory
In my research on Q-balls (a certain type of non-topological soliton) in cosmological backgrounds, I have obtained an equation that is nearly usable, except for one caveat. It would require me to ...
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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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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 ($c=1$)
$$ E = \int_{-\...
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How to derive the ODE from the EOM of vortex?
In the Lagrangian mode we have the equation of motion
\begin{align}
\partial_\mu F^{\mu\nu}&=j^\nu. \\
D_{\mu }D^{\mu}\phi +\mu^{2}\phi-\lambda(\phi^{*}\phi)\phi &=0.
\end{align}
Since we ...
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Why can you make $V$ stationary with respect to a parameter of the field in Derrick's theorem?
I'm going over Coleman's derivation of Derrick's theorem for real scalar fields in the chapter Classical lumps and their quantum descendants from Aspects of Symmetry (page 194).
Theorem: Let $\phi$ ...
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Dimension analysis in Derrick theorem
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe:
What I don't understand from the above statement:
why $e(\mu)$ has minimum for ...
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What does the Pontryagin index do in BPST instanton (solution to Yang-Mills theory)?
$$
\mathcal L = -\frac12\mathrm{Tr}\ F_{\mu\nu}F^{\mu\nu}+i\bar\psi\gamma^\mu D_\mu\psi
$$
We take this Lagrangian for QCD, after this I need to calculate BPST instanton with topological Pontryagin ...
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Obtaining the topological charge
I want to obtain the topological charge or winding number of the map
$$
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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Erik Lentz's faster-than-light soliton
It's well known that, in relativity, if you can go faster than light, you can go backwards in time and create a paradox.
Also, attempts to create "warp-drive" space-times in which something ...
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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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Asymptotic behaviour of soliton-antisoliton solution for the Sine Gordon equation
The question isn't about any actual homework, it's rather a (probably simple) intermediate step I've encountered on Rajaraman's Solitons and instantons : an introduction to solitons and instantons in ...
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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}$. ...
Buzz♦
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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,
$$...
Buzz♦
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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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Violation of Derrick's theorem for finite energy, time independent solutions?
How are vortices the finite energy time independent solutions for 2+1 dimensions abelian Higgs model? Doesn't it violate Derrick's theorem that there are no finite energy time independent solutions in ...
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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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Resources for Gravitational Soliton (specially on the Belinski–Zakharov transform)
Can someone provide some resources (books, notes, articles etc.) on Gravitational Soliton (specially on the Belinski–Zakharov transform)?
I've found only the following two reference from the Wikipedia ...
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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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Wave propagation speed in non-linear differential equations
Could it happen than a solitary travelling wave (soliton) had a different propagation speed when seen from the usual wave equations from that in a non-linear equation. I mean, suppose a solution $F=f(...
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Does a general soliton solution satisfy ALSO the normal wave equation?
I checked that the usual wave funtions of a gaussian pulse, a $\text{sech}(x-vt)$ and $\text{sech}^2(x-vt)$ solitons (the two latter from KdV equations) satisfy the wave equation.
Is this general? I ...
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Solitons and traveling waves for a Schrödinger type equation
I am a mathematician and not a physicist.
I came across a non--linear PDE whose linear part is a Schrödinger equation (i.e. a dispersive equation) and we know that this equation has a solution for $x\...
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If principle $SU(N)$ bundles on 3-manifolds are trivial, how can there be magnetic monopoles?
Magnetic monopoles are solitons, i.e. field configurations on space (which is 3 dimensional). In pure $SU(N)$ gauge theory, magnetic monopoles can be constructed via 't Hooft's abelian projection (...
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It is said that the dual Meissner effect can explain confinement, but where is the Higgs?
It is said that the dual Misner effect can explain confinement. This refers to when the monopole field acquires a v.e.v..
The t'Hooft-Polyakov monopole arises in a theory with a Higgs. So how does the ...
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What do monopoles have to do with strong coupling?
My understanding is that strong coupling effects arise from instantons in the path integral.
But I sometimes read that monopoles (see the electric-magnetic duality) can allow one to calculate strong ...
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Topological charge change in QFT
Is it possible for the topological charge to change in quantum field theory?
The proofs in the following paper: Quantum soliton operators for vortices and superselection rules
are all based on the ...
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Intuition behind focusing vs defocusing in integrable systems like NLS, KdV, mKdV
The following are examples of integrable systems arising from the AKNS system (check out AKNS paper here and a short Wikipedia description)
Non-Linear Schrodinger equation
Korteweg-de Vries equation
...
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Hopfion with only in-plane vortex rather than skyrmion along the torus?
A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we ...
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What is a difference between solitons and anyons?
In the article Creation and annihilation of mobile fractional solitons in atomic chains the authors claim that they prepared 1D solitons which can be used in topological quantum computing. Based on ...
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Why are non-perturbative solutions important and how to take them into account?
I am guilty of studying physics with an almost complete focus on the mathematical constructions (together with the motivating physical premisses) and ignoring the semantic physical intuition, which I'...
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Wave without trough?
Why does this video appear to show a wave with no trough? Do such waves exist?
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Questions on the Zakharov-Shabat inverse scattering paper
I am trying to work through the Zakharov and Shabat paper on inverse scattering for the nonlinear Schrodinger equation (PDF). I am stuck on section 2.
Problem 1. I need to know how to reconstruct $\...
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Can wrapped D-branes change the cycle they wrap, by quantum effects?
Suppose the internal manifold in a string compactification of type II, say, contains a D-brane wrapped around a given cycle. Is there an obstruction to the brane changing its wrapping cycle via a sort ...
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Can a kink in a finite one dimensional box tunnel into a trivial solution?
Given a simple kink solution of the Sine Gordon equation, is it possible for such a solution in a finite volume to tunnel into a trivial vacuum solution, given that such tunneling demands a finite ...
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Original BPS state paper by Bogomol'nyi
I've been searching for the original paper by E.B. Bogomol'nyi titled "The Stability of Classical Solutions" online, and have yet to find a resource which holds it. So far, the closest I've ...
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Differentiation of an operator equation in paper by Chen, Lee, Pereira 1979
This 1979 paper by Chen, Lee, and Pereira gives an operator $L$ satisfying
$$\dot L = [A, L],\tag{1}$$
where $A$ is another operator, and the dot denotes time differentiation. They then define $I_n = \...
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Hilbert transform in soliton paper
I asked this question over at the Mathematics SE, see here, but have not gotten any responses, so I figured I might as well try here as well. While the question is mathematical, it does appear in a ...
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Why can kink not tunnel to the vacuum, making it topologically stable?
Why can the kink
$$\phi(x)=v\tanh\left(\frac{x}{\xi}\right)$$
not tunnel into vacuum $+v$ or $-v$ (with spontaneous symmetry breaking in the vacuum)?
From the boundary condition, $\phi(x)\rightarrow \...
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$O(3)$ sigma model for lumps
I'm studying the $O(3)$ $\sigma$-model related to lumps through chapter 6 of Manton's book.
There appears that $$\mathcal{L} = (1/4)\partial _{\mu}\phi \cdot \partial ^{\mu}\phi + \nu (1-\phi \cdot \...
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How $\varphi^6$ potential of topological soliton kink and anti-kink are calculated?
how $\varphi^6$ topological soliton kink and anti-kink are calculated ?, what is an anti-kink?
$$L = -\frac{1}{4}F_{\mu\nu}^2− |\varphi|^6 − ieA_\mu(\varphi^\ast\partial_\mu\varphi−\varphi\partial_\mu\...
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A primer on topological solitons in scalar field theories
As the title suggests I want to learn more about topological solitons in scalar field theories. I am searching for a resource which is self-contained, in the sense that it also explains the ...
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Non-Perturbative Effects Of Soliton in Quantum Field Theory
I am reading Quantum Field Theory in a Nutshell by A.Zee. In Chapter 5 Section 6, Under the subtitle A nonperturbative phenomenon, He commented
"That the mass of the kink comes out inversely ...
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Can massive particles be seen as soliton solutions?
I wonder if the common relativistic wave equations contain a sort of soliton solutions, which might be considered as particle localisations.
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Can "solitons" be explained by linear wave equation? [duplicate]
In this Wikipedia page about the history of solitons, the author say that the observations made by Scott Russell "could not be explained by the existing water wave theories" at that time.
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How do you check the stability of a kink solution?
I am reading a nice introductory note by Hugo Laurell (http://uu.diva-portal.org/smash/get/diva2:935529/FULLTEXT01.pdf) but got confused on section 3.2.
He claims the stability of kink by expanding a ...
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Soliton solutions of the Gross-Pitaevskii equation
The Gross-Pitaevskii equation admits soliton solutions such as: $$\psi(x)=\psi_0 sech(x/\xi),$$
where $\xi$ is the healing length defined by: $\xi=\frac{\hbar}{\sqrt{m \mu}}$, with $\mu$ being the ...
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