Talk:Soliton
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[edit] How long solitons exist?
Could somebody tell what is maximal time of soliton's existence,especially magnetic or electromagnetic one? Also what is maximal energy that soliton could contain?
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[edit] Some suggestions
The inverse scattering transform technique is universally regarded as a landmark in the theory of partial differential equations and applied mathematics in general, so I think it amply deserves its own article, which this article should cite. The proposed article on inverse scattering should probably also mention applications to exact solutions of Einstein's field equations as well as to solving the Korteweg-de Vries equation and sine-Gordon equation.
I think this article should also mention the closely related concept of a completely integrable system, and the observation of Shiing-Shen Chern that these can be formulated in terms of appropriate flat (zero curvature) connections. ---CH
P.S. Hi, MarSch, I just noticed you seem to have a link to a web page owned by someone I know at the top of your user page! ---CH
- Yeah, I came across it and I thought that was a good place to store it. I don't know that person though. --MarSch 14:56, 24 Jun 2005 (UTC)
Someone should should add some info about other areas that solitons show up, like plasmas.
[edit] Photos?
Anyone got a decent soliton photo? Perhaps a tidal bore that's transitioned or a canal example...? UmptanumRedux 23:29, 30 June 2006 (UTC)
- I added a link to a great photo of a Soliton. --Nick 17:45, 6 July 2006 (UTC)
[edit] Relationship between a Standing Wave and a Soliton?
Could someone please add some text explaining the relationship between a Soliton and a Standing Wave? They seem to be intimately related. See how both are discussed in the article on Modelocking. For example, is it accurate to describe a Soliton as a "Travelling" Standing Wave? Or a Standing Wave as a Stationary Soliton? --Nick 17:44, 6 July 2006 (UTC)
[edit] Trek
In some Stare Trek TNG Episode, a soliton wave is used to propel a test ship, should that be put in?
- No. -- Jitse Niesen (talk) 03:28, 18 May 2007 (UTC)
[edit] Topological defects vs. solitons
The article states that solitons belong to a class of phenomomena known as "topological defects". I'm not sure that this is true for all solitons. I think that there may be some solitons (such as the soliton solution to the nonlinear Schrodinger equation) that cannot be described as topological solitons - although I am not certain of this. Does anyone know if this is the case? 129.234.4.10 17:21, 14 September 2007 (UTC)
- See Q-balls. There instead of a conserved topological charge, there is a different kind of charge Q (for instance, a Noether charge associated with U(1) symmetry) that prevents the disturbance from dissipating. Steve Avery (talk) 00:38, 14 January 2008 (UTC)
In relativistic field theories is often assumed (see e.g. T.D.Lee 1992) that all solitons belong to one of these groups: i) Topological solitons, where there exist a conserved charge of topological nature (due to the existence of non-trivial boundary conditions at spatial infinity) preventing the dissipation of the soliton ii) Non-topological solitons, where the conserved charge is not due to topological reasons but to other properties of the system, as an invariance of the lagrangian (e.g. Q-Balls with a U(1) symmetry), the existence of a singularity at the origin in the form of a Dirac-delta function allowing a charge-definition (as in the Born-Infeld theory) and other. In this sense the notion of topological defects is usually identified to that of topological solitons (although some authors find subtle differences between both concepts). Kaycopperfield (talk) 23:04, 15 February 2008 (UTC)
