What are solitons and how do they affect us?

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Discussion Overview

The discussion revolves around the concept of solitons, their definitions, and their implications in various contexts, including optical fibers and ocean waves. Participants explore theoretical aspects, historical references, and personal experiences related to soliton phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Historical

Main Points Raised

  • Some participants describe solitons as non-periodic waveforms and reference the Korteweg-de Vries equations as foundational to their understanding.
  • Others mention the Bloch equations in relation to optical solitons, noting that these are exceptions to the KdV framework.
  • One participant shares a personal anecdote about a missed opportunity to observe a water wave soliton in a university wave tank, expressing uncertainty about the reasons for the cancellation.
  • There is a discussion about the nonlinear Schrödinger equation also producing solitons, particularly in the context of ocean waves, with references to "killer waves."
  • Participants note the historical significance of solitons, including their original observation in canals and the concept of lossless propagation.
  • Spelling corrections and clarifications are made regarding the names of equations and terms related to solitons, indicating a collaborative effort to refine the discussion.
  • There is a playful exchange regarding the correct spelling of "rogue" waves, highlighting the informal nature of the conversation.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and knowledge about solitons, with some clarifying terms and equations while others share differing views on their effects and occurrences. No consensus is reached on the broader implications of solitons in natural phenomena.

Contextual Notes

Limitations include potential misunderstandings of the equations involved, the informal nature of personal anecdotes, and the lack of detailed exploration into the implications of solitons in real-world applications.

Mk
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What are solitons and how do they affect us?

I found out in 1973, Akira Hasegawa of AT&T Bell Labs was the first to suggest that solitons could exist in optical fibers. He also proposed the idea of a soliton-based transmission system to increase performance of optical telecommunications.
 
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A soliton is essentially a singleton, non periodic wave form. You may want to investigate the Korteweg-de Vries [edit spelling re Marlons post] equations as they form the basis for most solitons. Optical solitions are an exception to that, they arise out of the Bloch equations. [Edit: spelling corrected re Tide's post]. It has been a long time since I studied this so perhaps others will be able to bring fresh material to the front.

The university (Oregon St. U) I was attending has a world class wave tank facility, our class (grad level Math modeling) was promised a trip to the wave tank where they would generate a water wave soliton for us. Unfortunately, it never happened, I am not sure whether it was mechanical troubles or simply not being able to spare wave tank time to configure for solition generation.

As for how they effect us, I would say that they are an extremely rare natural event, or generated in a lab, so there is little or no effect that I know of.
 
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Integral, i am sure you wanted to refer to the "Korteweg-de Vries equation"...

marlon
 
Only a Belgian (or possibly, a Dutchman) could get those names right..:wink:
 
marlon said:
Integral, i am sure you wanted to refer to the "Korteweg-de Vries equation"...

marlon

THAT'S IT! That is the way it should be spelled! My spelling remark was in reference to both the Block equations and the Korteweg-deVries. Thanks for the correction.
 
In googling, you often find the abbreviation KdV is used. They are not the only equations that produce solitons; the nonlinear Scroedinger equation also does, relevant to solitons in the open ocean (possible candidates for "killler waves"), and there are others. Lax developed a way to transform these different equations into each other. See Lax Pairs. A great deal of very productive research has been done on this stuff over the last 60 years, since the Fermi-Pasta-Ulam (FPU) paradox attracted attention to soliton solutions beyond canals.

A little more detail on how a soliton comes about.

There are two things that happen to an ordinary wave in a nonlinear medium; it tends to spread out as Fourier components of different frequency travel at different speeds, and it tends to crest as some components approach the maximum speed possible. These effects are in opposite directions and it is possible that they may be in exact balance, in which case the wave does not change shape. This is a soliton.
 
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SelfAdjoints reference to the canals brings to mind another key feature of Solitions, lossless propagation.

They were originally observed as singleton water waves which traveled for miles in canals.
 
Incidentally, it's the Bloch equation! :-)
 
Once again, Thanks for the spelling help. I have this very frustrating ability to recognize that something is misspelled, but some how lack the ability to find the correct spelling. Just ask Tom about my spelling ability! :smile:

IIRC that was Ernst Bloch.

I'll fix it in the original post.
 
  • #10
selfAdjoint said:
the nonlinear Scroedinger equation also does, relevant to solitons in the open ocean (possible candidates for "killler waves"), and there are others. Lax developed a way to transform these different equations into each other. See Lax Pairs.
Yes, I was reading about killer/freak/monster/rouge waves, and that's where it came up, thanks all.
 
  • #11
"rouge" or "rogue"?
 
  • #12
Gonzolo said:
"rouge" or "rogue"?
Yes, "rogue," thank you. "Rouge" happens to be a red colored cosmetic.
:biggrin:
 

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