# What is a soliton?

hanson
Hi all.
Can somone explain me the difference between "soliton" and those "normal waves" i learn in highschool physics?
I can't really distinguish between them.
While a soliton travel at a constant shape and velocity, doesn't the same apply to normal waves?
That two solitons collide and retore theirs own shapes afterwards, doesn't this apply to normal waves? the principle of superposition? I know there will be phase different introduction in the collision of solitons.
But why are solitons so special?

Find kindly explain.

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The collision between two solitons is analogous to the collision between two billiard balls. That is not true of the behaviour of ordinary wave trains.

Furthermore, most water waves are DISPERSIVE, except in the special case of linear waves in the shallow water limit.
Otherwise, water waves experience both wavenumber and amplitude dispersion.

A Soliton is a non-dispersive NON-linear phenomenon.

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nithin
wow first time hearing that word ... cant seem to find much about it on that word or in my Serway book. Where did you come across that term?

kendr_pind
a soliton is a giant wave which doesnt get obstructed by anything...it destroys anything in its path...it keeps on increasing in its intensity...a soliton might typically occur when a meteorite hits oceans...

hanson
a soliton is a giant wave which doesnt get obstructed by anything...it destroys anything in its path...it keeps on increasing in its intensity...a soliton might typically occur when a meteorite hits oceans...

Why doesn't it get obstructed by anything?

hanson
The collision between two solitons is analogous to the collision between two billiard balls. That is not true of the behaviour of ordinary wave trains.

Furthermore, most water waves are DISPERSIVE, except in the special case of linear waves in the shallow water limit.
Otherwise, water waves experience both wavenumber and amplitude dispersion.

A Soliton is a non-dispersive NON-linear phenomenon.

Collision between two billiard balls? What does it mean? can u further elaborate on this?

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Don't mix a "freak wave" with a "soliton" kendr pind! It has nothing to do with it.

Remember that a soliton's velocity is an increasing function of its height (this is a non-linear effect).
If a higher soliton overtakes another travelling in the same direction, what you will see is the following:

Gradually, the height of the soliton in front increases, whereas that of the one behind decreases. This happens until the soliton in front is exactly as high as the one behind was, and that has been lowered correspondingly.
Thus, we can regard this as an ideal transfer of momentum from the latter soliton to the one in front, as we would see in an analogous billiard ball situation.

J77
Yeah -- solitons can be tiny.

You can form one experimentally in a water flume -- when the wave of water hits the end of the flume, you can see soliton-type solutions travel back, along the flume's bed.

They're also frequent in nonlinear optics -- a proposed way on which to transmit data.

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Also, the behaviour of solitons is NOT that according to the principle of superposition. That is a LINEAR phenomenon.

Two meeting solitons RETAIN THEIR INDIVIDUALITY AT ALL TIMES, in particular, there exists no moment when their crests coincide. They just transfer their momentum to the other.

hanson
so, will a soliton decay? i mean obstructable...?

Also, would u have recommendation on any introductory books on the subject?

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Now, the soliton solutions is typicallly a feature of INVISCID flow, i.e, viscosity is regarded to be negligible. This is a perfectly good approximation for say, open channel/river flow, or ocean movements over a long period.

More important is the effect on the wave patterns due to the depth profile.
If there are significant changes here, then this will be reflected in changes of the surface wave patterns; i.e, a stable phenomenon like a soliton will break up.
(In nature, we can typically see soliton formations and propagation in broad, lazy rivers, like the English Severn.)

Ordinary waves diffract and disperse as they propagate. Solitons on the other hand have these diffractive and dispersive tendencies balanced via some nonlinear effect that allows the solitons to retain their shape as they propagate.

Optical solitons for example retain their shape via the nonlinear Kerr effect, which essentially causes the wave to focus itself as it propagates. This self-focusing counter-acts dispersion, resulting in dispersion-free propagation, which is why solitons may be useful in data transmission as J77 mentioned.

Claude.