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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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 $I_n = \...
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Hilbert transform in soliton paper
I asked this question over at the Mathematics SE, see here, but have not gotten any responses, so I figured I might as well try here as well. While the question is mathematical, it does appear in a ...
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$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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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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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 "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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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 ...
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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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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 ...
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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 ...
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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 ...
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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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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 ...
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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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How to Diagonalize Self-Interacting Scalar Hamiltonian for Mass Term from Polyakov Paper?
So, I'm reading through Polyakov's paper from 1974, "Particle Spectrum in Quantum Field Theory." I'm trying to work through all of the steps and properly understand everything. For context, ...
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Peak splitting in one-component reaction–diffusion equations
I am studying a one-component reaction–diffusion equation:
$$ \partial_t u(x,t) = D \partial^2_x u(x,t) + R\left(u(x,t)\right)$$
Looking at systems that exhibit a peak solution (solitary localized ...
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Spontaneous discrete symmetry breaking always implies domain walls
I've read several times that if a discrete symmetry is spontaneously broken, then there exist domain walls that interpolate between the different vacua. However, Weinberg says that if the former ...
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Sum of topological charges is the Euler characteristic
I have seen many places claiming that the given a collection of topological defects on a 2-dimensional surface, the sum of the topological charges is $2\pi\chi$ (where $\chi$ is the Euler ...
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Stability and topological charge of kink (anti-kink) solutions (soliton)
I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution.
First, we have a $1+1D$ spacetime model
\begin{...
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Must a field approach one of its vacua to have finite energy?
I'm reading these Cornell lectures on solitons (link doesn't work right now, but it just worked yesterday), and I can't seem to prove what I thought would be a simple analysis exercise.
Namely, ...
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Soliton solution of the NLS equation
My understanding of soliton - it is a moving pulse in a medium which does not change its structure with time. It has other properties like no interaction with other solitons (this could certainly be ...
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Completely Integrable Frustrated Lattice Systems
The Toda lattice is a prime example of a lattice system that is completely integrable, in the sense that it admits a Lax pair,
https://doi.org/10.1143/PTP.51.703,
making it easy to find soliton ...
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Set of zeroes as coset space
I am currently studying Chapter 6 of Coleman S. - Aspects of Symmetry.
We study a spontaneously broken gauge theory in two spatial dimensions where the Lagrangian reads:
$$
\mathcal{L} = -\frac{1}{4}...
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