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3
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2answers
47 views

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 ...
8
votes
0answers
115 views

$\phi^4$ 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 \...
0
votes
2answers
105 views

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 ...
2
votes
2answers
168 views

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 ...
3
votes
2answers
270 views

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 ...
1
vote
1answer
51 views

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(...
9
votes
2answers
301 views

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 ...
2
votes
0answers
29 views

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 ...
3
votes
1answer
84 views

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 $\...
1
vote
2answers
429 views

Derrick’s theorem

Consider a theory in $D$ spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
7
votes
2answers
283 views

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 ...
1
vote
0answers
70 views

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 ...
2
votes
1answer
86 views

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 ...
1
vote
0answers
60 views

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: ...
5
votes
2answers
89 views

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 ...
1
vote
1answer
31 views

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 ...
0
votes
0answers
36 views
2
votes
0answers
77 views

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 ...
1
vote
0answers
115 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
0
votes
0answers
26 views

Dirac equation in the presence of a defect

The 1D Dirac equation in the presence of a defect is described by a position dependent mass term known as a "kink" or "soliton". It is sign changing and tends to a constant at positive and negative ...
1
vote
1answer
214 views

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 ...
1
vote
2answers
107 views

Why Kink can not tunnel to vacuum, and is topologically stable?

Why the kink $$\phi(x)=v\tanh(\frac{x}{\xi}) ,$$ can not tunnel into vacuum $+v$ or $-v$ (Spontaneous symmetry breaking vacuum). From the boundary condition ($x\rightarrow \pm\infty, \phi(x)\...
12
votes
1answer
792 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, $$(i\...
1
vote
1answer
34 views

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 ...
2
votes
1answer
172 views

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 ...
2
votes
1answer
45 views

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 ...
0
votes
1answer
299 views

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, ...
0
votes
1answer
100 views

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.
1
vote
0answers
116 views

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?
2
votes
0answers
48 views

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, ...
1
vote
1answer
234 views

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 ...
1
vote
1answer
705 views

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 ...
3
votes
2answers
273 views

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 ...
14
votes
1answer
608 views

Does the existence of Higgs imply the existence of Magnetic Monopoles?

I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the ...
2
votes
0answers
108 views

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 ...
2
votes
0answers
76 views

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 ...
24
votes
1answer
749 views

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 ...
6
votes
0answers
401 views

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 ...
1
vote
0answers
89 views

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 ...
7
votes
1answer
374 views

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 ...
2
votes
1answer
189 views

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 ...
0
votes
1answer
73 views

Are solitons an example of collective motion?

Are solitons an example of collective motion?
1
vote
1answer
242 views

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 ...
1
vote
1answer
191 views

Type I' String theory as M-theory compactified on a line segment?

I was considering the S-dual of the Type I' String theory (the solitonic Type I string theory). That is the same as the S-dual of the T-Dual of Type I String theory. Then, that means both length ...
0
votes
1answer
197 views

Vortex in D dimensions soliton

let us consider the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows represent the magnitude of φ, while their directions indicate the orientation in the $φ_1 -φ_2$ plane. ...
2
votes
3answers
121 views

Valid theory in all dimensions for solitary waves

I'm studying soliton (solitary waves). They are many theory which explain the phenomenon, like sine-Gordon model. But sine-Gordon model has limitations when it applies to 4 dimension because it is ...
0
votes
0answers
314 views

Domain wall and kink solutions from solitions equations

A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$ where $x_0$ is a constant of integration when we drived this ...
1
vote
1answer
228 views

Solving the soliton equation without energy

In this passage from Srednicki's Quantum Field Theory (page 576) The solution of interest is time independent, so we can set $\dot\varphi = 0$. We can also rewrite the remaining terms in $E$ as \...
1
vote
1answer
218 views

Potential in Relativistic Scalar Field Theory

My intention is to establish a Soliton equation. I have cropped a page from Mark Srednicki page no 576. I have understand the equation (92.1) but don't understand that how they guessed the ...
7
votes
1answer
142 views

Do instantons support quantum bound states?

When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...