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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 ...
monday's user avatar
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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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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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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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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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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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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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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 ...
Martin Vesely's user avatar
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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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2 votes
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Wave without trough?

Why does this video appear to show a wave with no trough? Do such waves exist?
Abdullah is not an Amalekite's user avatar
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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 ...
Bastam Tajik's user avatar
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2 votes
1 answer
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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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2 answers
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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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5 votes
3 answers
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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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$O(3)$ 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\...
Juan Carlos Dominguez Solis.'s user avatar
1 vote
1 answer
504 views

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 ...
Juan Carlos Dominguez Solis.'s user avatar
1 vote
1 answer
160 views

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 ...
1 vote
1 answer
145 views

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 ...
Tan Tixuan's user avatar
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0 answers
33 views

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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1 answer
636 views

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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Warp drive small scale experiments "proof of concept" [duplicate]

Possible small scale warp drive experiments, or small scale experiments with quantum mechanics to model space-time warping? Why is it so difficult to engineer a small scale warp drive even though ...
Local45953's user avatar
9 votes
3 answers
3k views

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 ...
Mitchell Porter's user avatar
2 votes
0 answers
131 views

Testing space-time warp on a smaller scale, "Breaking the Warp Barrier: Hyper-Fast Solitons in Einstein-Maxwell-Plasma Theory" [duplicate]

So according to this paper it creates a warp drive without the need of negative energy to operate which many think does not exist in reality. So my question is what would you do to experimentally ...
Local45953's user avatar
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0 answers
39 views

Do you know about any book which discusses solitons in Benjamin-Ono Equation?

Benjamin-Ono equation is an integrable equation with soliton solutions. There are many books on solitons. The ones I know about mainly discuss solitons in Korteweg de-Vries and related equations. Do ...
2 votes
2 answers
325 views

Are cross sea waves solitons?

Last week I went to the sea and observed some waves of the type pictured here By Michel Griffon - Own work, CC BY 3.0, Link And I wondered if they were solitons or not. I've seen more than once ...
rootofunity's user avatar
2 votes
1 answer
398 views

An instanton in $d$ dimensions is often a soliton in $d + 1$ dimensions?

The title of this questions is a "folklore" I've heard from a lot of researchers, but I never understood why this is the case. I know what an instanton and soliton is, respectively in the ...
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3 votes
1 answer
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Period behavior near separatrix in Hamiltonian system

Given the periodic potential Hamiltonian $H=\frac{p^2}{2} - \omega_0^2 \cos(q)$ I would like to show that near the separatrix the period has this behavior: $T(E)\sim |\log(\delta E)|$ with $\delta E=|...
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Boundary conditions for radial solution of gauged topological vortices

I am following the book Topological Solitons by Manton and Sutcliffe and I am struggling to understand a boundary condition they choose to find the radial solutions of gauged vortices with finite ...
Fernando Torre's user avatar
1 vote
1 answer
100 views

What are the two different $\mathbb{S}^n$ in the construction of the homotopy group $\pi_n(\mathbb{S}^n)$ that classifies topological defects?

According to Mukhanov's Physical Foundations of Cosmology, Homotopy groups give us a useful unifying description of topological defects. Maps of the $n$-dimensional sphere $\mathbb{S}^n$ into a ...
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