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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Boundary condition for solitons in 1+1 dimensions to have finite energy
Suppose a classical field configuration of a real scalar field $\phi(x,t)$, in $1+1$ dimensions, has the energy $$E[\phi]=\int\limits_{-\infty}^{+\infty} dx\, \left[\frac{1}{2}\left(\frac{\partial\phi}...
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Vacuum Manifold of an $SU(2)$ Theory
I am reading Coleman's book "Aspects of Symmetry", specifically chapter 6 "Classical Lumps and their Quantum Descendants". He gives an Example 5 p. 209 for the topological solutions for an $SU(2)$ ...
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How is the velocity of a soliton defined?
The equation of motion of a real scalar field $\phi(x,t)$ in 1+1 dimension in an arbitrary potential $V(\phi)$ is given by $$\frac{\partial^2\phi}{\partial t^2}-\frac{\partial^2\phi}{\partial x^2}+\...
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Describing travelling waves carrying energy from one point to another
A simple harmonic wave in one-dimension (for simplicity) $y(x,t)=A\sin(\omega t-kx)$ in a medium is often presented as an example of a travelling wave. But such a plane wave is infinitely extended ...
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What is the definition of soliton?
What is the definition of soliton? I've encountered this name in different situations like when the topic discussed is about QFT, fluid dynamics or optics, but I cannot find a general definition. I've ...
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Solving Higher-Order Kinetic Energy Term (Gross-Pitaevskii equation) [closed]
Consider now propagation of non-linear waves in one-dimensional chain of dimers governed by the non-linear Schrödinger equation for the normalized wave envelope $\Psi(x,t)$,
$$
i \frac{\partial \Psi}{...
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Characteristics of wavepackets
I've been learning about wave packets and group velocities recently and had a question. Using simple trigonometric identies, we can show that the super position of two traveling waves with frequency-...
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Non-topological solitons in condensed matter physics
As I know most well-known soliton solutions in condensed matter physics are topological ones: kinks, domain walls etc.
In field theory there are several examples on non-topological solitons: Q-balls, ...
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Do plane waves exist in nature? [duplicate]
Drop a stone in the pond...a wave propagates radially from the source. The conservation of energy says the wave must decay proportionally to the radial distance. If I drop a steel I-beam in the pond, ...
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Nonlinear Saturated Schrodinger Equation in 1D- Physical Models
I'm studying the Nonlinear 1d Schrodinger equation
$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$
and specifically, its solitary ...
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Can localized fluid perturbations be accelerated by pressure gradients?
I would like to know if there are any examples in fluid dynamics (or continuum dynamics) of small perturbations (or waves, solitons, or other "localized" solutions of the fluid) being accelerated in ...
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$\phi^4$ theory kinks as fermions?
In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
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From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?
In the framework of QM, we have known that particle, like electron, cannot be a wavepacket, because if it is a wavepacket then it will become "fatter" due to dispersion and it's impossible.
However ...
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Left-right topology
Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking
\begin{equation}
SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to SU(...
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Why do vortices scatter at right-angles
I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him.
In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ...
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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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Mathematical understanding of vortex solitons
I am wondering if anyone has ever come up with a mathematical description of something that (to me, and I am no expert) look like soliton vortexes.
The example I can think of is if you create two ...
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Few basic questions about instantons
For the $SU(2)$ Yang-Mill's theory, (1) how can one understand that the finite action solutions of the Euclidean equations of motion (called Instantons) exhibit tunneling effects? (2) Since, this ...
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Question from Terning's book
In Chapter 7 of Terning's book (Modern Supersymmetry), the first example considered is that of an $SO(3)$ gauge theory, a complex scalar in the triplet representation of $SO(3)$ and a potential term:
$...
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What is beam confinement?
In the context of the propagation of an electromagnetic wave and optical vortex solitons, I came across the term "beam confinement". Particularly, beam confinement requires the amplitude of the ...
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How do instantons look in real time/spacetime?
Instantons, as I understand it, are mathematical constructions in Euclidean spacetime. Does it imply that instantons do not exist in real spacetime or the instanton tunneling effects does not have ...
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Sine integral as a soliton profile?
Among the most commonly known 1+1 soliton/solitary-wave profiles are:
$\tan^{-1}(\exp(x-vt))$ for Sine-Gordon,
$\tanh(x-vt)$ for $\phi^4$,
$\operatorname{sech}^2(x-vt)$ for KdV.
My question is: ...
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Distinction of Dirac monopole and Polyakov-'t Hooft monopole
Can anybody explain the physical difference between Dirac monopole and Polyakov monopole?
First, let me write down what I know briefly.
Dirac monopole
It comes from the symmetry of Maxwell ...
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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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Soliton solution for a diffusive system [closed]
With a simple model for bacterial diffusion, I get this partial derivative equation :
$$\frac{\partial n}{\partial t} = D\frac{\partial^2 n}{\partial x^2} + d_1 n -d_2 n^2$$
where $n(x,t)$ is the ...
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Why is the solution of the $\phi^6$ potential not a soliton?
Consider a theory with a $\phi^6$-scalar potential:
$$
\mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2.
$$
I solved its equation of motion but found that the general form of its ...
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Soliton wave transmission and experiments
What are Solitons?
Does energy transfer without interference in Solitons?
I read first about in connection with Breather surface of constant negative Gauss curvature $K$.
Are there physical laws ...
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Solitons and its infinite extension
A soliton, for example the KdV equation solution, has the profile proportional to a hyperbolic secant squared ${\text{sech}}^{2}(x-ct)$. And since it is hyperbolic it has an exponential dependence, so ...
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Are there resources for simulating and/or theoretically describing solitons?
Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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Besides vortex rings, are there other types of traveling waves that can carry matter as well as energy?
Vortex rings are a special soliton wave that are known to carry matter over a distance as well as energy. This can easily be demonstrated using a cardboard 'vortex canon' filled with smoke. The smoke ...
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difference between classical vacuum solutions and instantons
What does the classical vacuum of the $SU(2)$ Yang-Mills action correspond to? Does it correspond to $F_{\mu\nu}=0$ everywhere or just at the spatial infinity? In Srednicki’s book, he has shown that, ...
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Explanation of the waves on the water planet in the movie Interstellar?
We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions.
Simple [hopefully] Pre-questions:
1) If the water ...
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Speed of an electromagnetic soliton in free space
What is the speed of an electromagnetic soliton in free space? Is it equal to 'c' ?
P.S. My understanding of the Fourier transform says it's not.
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Phase and group velocity of a soliton? [closed]
How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
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Categorization of electromagnetic solitons?
I've seen over the years several mentions of electromagnetic solitons that appear in the high-intensity regime (where vacuum polarization becomes important). Some of these are coupled with plasmas, ...
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Moduli spaces in string theory vs. soliton theory
In both string theory and soliton theory, moduli spaces are frequently used.
As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for ...
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About solitons, what is the difference between kinks and vortices?
I am reading papers about solitons for my small reports, and i could not understand its physical meaning in detail.
I know soliton is solitary wave which behaves like particle. And many text they ...
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Domain walls intersection
I was reading this article(On domain shapes and processes in supersymmetric
theories). In the paragraph about domain walls intersection (paragraph $4$, page $7$) the authors say:
In a one-field ...
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No monopoles in the Weinberg-Salam model
I'm reading Chapter 10.4 on the 't Hooft-Polyakov monopoles in Ryder's Quantum Field Theory.
On page 412 he explains why magnetic monopoles cannot appear in the Weinberg-Salam model.
I'm I right by ...
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KdV equation and classical linear wave equation
Like we know, the standard form of KdV equation is
$$u_{t}-6uu_{x}+u_{xxx}=0,\tag{1}$$
where this equation describes a solitary wave propagation and $u=u(x,t)$.
On the other hand, we know the ...
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Soliton Moduli Spaces and Homotopy Theory
The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$
and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu F^{\...
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$AdS_3$ soliton of Witten - for Hawking-Page transition
Are there explicit AdS$_3$ soliton solution?
in the sense of Witten's Anti De Sitter Space And Holography and Hawking-Page transition paper, by doing a
$$\tau_E, y ,r \to y, \tau_E ,r$$
from a ...
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Fractional quantum number induced in a soliton profile
It has been known there is fractional quantum number induced in a soliton profile, such as this Jeffrey Goldstone and Frank Wilczek paper and many works of Jackiw.
For example the electric charge ...
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Nomenclature clarification concerning solitons
My experience with solitons is restricted to the classical setting, namely solutions to the quartic interaction $\phi^4$, the Sine-Gordon equation, and Korteweg–de Vries equations. I was explicit to ...
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Is optical-illusion responsible for Loch Ness monster? [closed]
When you look out at the white-caps on a wind-swept lake, you can see a dark, undulating pattern under the crests of the white-caps.
Could this shadow-like area explain the sightings? Revised, see ...
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Is there a consensus on the definition of wavelength for a solitary wave?
Solitary waves are by definition a wave of single nature so the usual definition for periodic waves does not apply. R. Dalrymple provides a definition but I saw a lot of other websites and papers ...
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Causes of hexagonal shape of Saturn's jet stream
NASA has just shown a more detailed picture of the hexagonal vortex/storm on Saturn:
http://www.ibtimes.com/nasa-releases-images-saturns-hexagon-mega-storm-may-have-been-swirling-centuries-1496218
...
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Magnetic field lines and knots
As I was reading the book The Trouble With Physics, I encountered a small paragraph which seemed bit confusing. The paragraph goes as follows:
Picture field lines, like the lines of magnetic field ...
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Why linear wave equation does not have solitonic solutions?
As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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