Solitons

[Mk]

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.

[Integral]

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.

[marlon]

Integral, i am sure you wanted to refer to the "Korteweg-de Vries equation"...

marlon

[arildno]

Only a Belgian (or possibly, a Dutchman) could get those names right..:wink:

[Integral]

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.

[selfAdjoint]

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.

[Integral]

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.

[Tide]

Incidentally, it's the Bloch equation! :-)

[Integral]

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.

[Mk]

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.

[Gonzolo]

"rouge" or "rogue"?

[Mk]

"rouge" or "rogue"?
Yes, "rogue," thank you. "Rouge" happens to be a red colored cosmetic.
:biggrin: