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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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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$O(3)$ 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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When you say "stability of soliton in energy space" what is energy space?

I am reading this (https://arxiv.org/abs/0802.2408) excellent review of the stability of the solutions of the differential equations. However, I don't quite understand what the author means when ...
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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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Doubt on Lax formulation of Korteweg–de Vries equation

The Korteweg–de Vries equation is given by: $$\frac{\partial u(x,t)}{\partial t}-6u\frac{\partial u(x,t)}{\partial x}+\frac{\partial^3 u(x,t)}{\partial x^3}=0$$ This equation can be formulated using ...
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Spin of skyrmion

Baryons can be considered as solitions in Skyrme model(See also this post.): Such Lagrangian haven't any information about number of colors. Bosonic or fermionic nature of baryons depends on number ...
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Periodic traveling waves of the form $\phi(x,t)=\psi_c(x-ct)$ for a $\phi^4$ model

Consider \begin{equation}\label{1} \partial^2_t\phi-\partial^2_x\phi=\phi -\phi^3,\: \ (x,t) \in \mathbb{R}\times \mathbb{R} \hspace{30pt}(1) \end{equation} the $\phi^4$ model. I know that $$H(x)=\...
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Theory on domain walls

In Baryons in Quantum Chromodynamics, Zohar Komargodski have slide: I wanna understand: Why domein wall can have nontrivial worldvolume theory? When such solitonic objects have interior degrees of ...
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Quantum solitons: derivation of $ \int {\phi^\prime}^2 dx = M$ using Lorentz invariance

I was reading through page 10 of this document (Chua, 2017) on quantum solitons, and came across the following statement relating to the equation for kinetic energy $$T = \left(\frac{da}{dt}\right)^2\...
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An interesting observation: Ordered, up and down movement of vortex rings in water

I was watching a video on David Tong's research work when I stumbled upon a peculiar movement of vortex rings in water. Around the 1:20 time mark, Baths and Quarks: Solitons explained, David Tong uses ...
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Intuition about ADHM construction

I'm trying to understand reasons, why self-dual Yang-Mills equation can be reduced to algebraic equations. It's seem like a miracle. In article Construction of Instanton and Monopole Solutions and ...
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In which representation are monopoles of grand unifying theories classified?

In the context of grand unification theories A.Zee's book states that $SU(5)$ (or $SO(10)$ if $SU(5)$ is considered as outdated as GUT candidate) as GUT and as spontaneously broken non-abelian gauge ...
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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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What does topologically stable mean?

I am working on an article about skyrmion manipulation and it is written that those particles are "topologically stable particle-like spin configurations that carry a characteristic topological charge ...
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How does the $U(1)$ global symmetry break in the gauged $XY$ model?

I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks. gauged XY model: $\...
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4 votes
1 answer
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Is there a difference between topological defects and topological soliton?

Is there a difference between topological defects and topological soliton? Or are these objects the same thing? I ask this because it very common find some papers whose the authors itself refer, for ...
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Will tsunami waves travel forever if there was no land?

If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
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How solitons are related to particle physics?

Recently, I read a paper about introduction to solitons. Author said that the solutions of sine-Gordon equation can be candidate for modeling elementary particles and there are some applications in ...
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2 answers
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Different between droplet and a soliton

I am working on the droplet state in a Bose-Bose mixture. I have a question about the difference between the droplet liquid state and the soliton state: How we can treat a droplet state? And how do we ...
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Why do we consider solitons as a composite object?

Can someone explain why do we consider solitons as a composite object? I know that there are dual theories which the role of fundamental and solitonic objects can be mapped to each other, but I can't ...
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Can inhomogeneity in the medium accelerate particles

Suppose I have a charge which is moving in through a medium with constant velocity. Now, what will happen to the charge as it encounters an inhomogeneity in density? whether it will accelerate or ...
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