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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Finding the energy of a solution to the Sine-Gordon equation
I am delving into Quantum-Field Theory, and am stuck trying to work out how to compute the energy of a soliton solution to the Sine-Gordon equation in 1-1 spacetime.
I start with the Lagrangian ...
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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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How to use Belinsky-Zakharov transformation
I know it might be trivial. When using BZ transformation [1] to generate soliton solutions of Einstein’s field equations, one need a seed solution $g_{0}$ which gives $A_{0}$ and $B_{0}$. Taking them ...
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Can massive particles be seen as soliton solutions?
I wonder if the common relativistic wave equations contain a sort of soliton solutions, which might be considered as particle localisations.
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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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M branes/D branes are solitons?
I'm really confused.
In M theory/String theory, the fundamental objects are M/D branes. However, branes by defintion are just solitons. Solitons are just waves that maintain there shape.
So if a ...
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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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Violation of Derrick's theorem for finite energy, time independent solutions?
How are vortices the finite energy time independent solutions for 2+1 dimensions abelian Higgs model? Doesn't it violate Derrick's theorem that there are no finite energy time independent solutions in ...
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Applications of Optical Solitons
It is well known for the past 50-60 years that intense laser beams can form into soliton/solitary waves. Those exist either spatially in CW beams or temporally in ultra-short pulses, and their ...
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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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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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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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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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