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Nonlinear field theories contain a large number of localized solutions.

I have found this text in a article. What I don't understand is "what is localized?". Is it refer defining position of a particle or a wave? Can someone give me an elaboration with example?

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I would guess that the article is referring to solitons. I'm not sure if every non-linear system gives soliton solutions, but many do. The Wikipedia article I've linked gives lots of examples of classical solitons, but I'm not sure to what extent (if at all) they're important in the Standard Model. Perhaps one of the QFT specialists hereabouts could comment.

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  • $\begingroup$ But what the meaning of localization? $\endgroup$ – Raisa Aug 16 '13 at 16:18
  • $\begingroup$ @Raisa - have a read through the Wikipedia article on solitons and see if that helps. In QFT there are also instantons that are localised in both space and time. $\endgroup$ – John Rennie Aug 16 '13 at 16:52
  • $\begingroup$ Aha, I've just followed the link in your comment and it's an article about solitons and instantons. "Localised" simply means the solution is non-zero over a finite (usually small) region of space. Normally this would be applied only to a wave like solution localised in space, rather than e.g. a hydrogen atom that is certainly localised in space but not a wave like solution. $\endgroup$ – John Rennie Aug 16 '13 at 17:10

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