# What is soliton

I am new to this word.. This is not research level problem and it is soft question in nature. Just for curiosity, i am asking..

In literature, i am finding following words:(Wikipedia+ others).

Soliton is a self-reinforcing solitary wave

Solition is a phenomenon.

Solition is a property

Solitonic solution

As wikipedia also says, single definition is difficult to find. Can somebody explain this term according to you... It will be better if you give the idea of Soliton more mathematically rather only intuitively.

More precisely my question is WHAT IS SOLITON.

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For what it's worth, here's the Oxford English Dictionary definition: "a travelling, non-dissipative wave which is neither preceded nor followed by another such disturbance." Citation: "solitary, adj.". OED Online. December 2011. Oxford University Press. 5 March 2012 <oed.com/view/Entry/184311>;. – Tanner Swett Mar 5 '12 at 19:05
@TannerL Swett, so oxford definition matches with Wikipedia... Thanks for the commment. – zapkm Mar 5 '12 at 19:26

A soliton (at least in my field) is a 'self-similar solution' to a PDE. For instance a solution $(g_t)$ to the Ricci flow equation $$\frac{\partial g }{ \partial t} = - 2 \mathrm{Ric}(g(t))$$ is a Ricci soliton if it takes the form $g(t)= \alpha (t) \phi_t^* (g(0))$ where the $\alpha(t)$'s are scalars and the $\phi_t$'s are diffeomorphisms, i.e. the metric at time $t$ differs from the initial metric by the action of diffeomorphisms and/or dilation.

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Thanks.. i never thought this way for soliton... – zapkm Mar 5 '12 at 19:22

There is the historical and theoretical survey "The Symmetry of Solitons" by Richard Palais.
I have liked it very much, so I hope you can find it useful.

Bye.

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Thanks for the link... i will look upon this.. – zapkm Mar 5 '12 at 19:23
Also in the Bulletin is Terry Tao's "Why are solitons stable" ams.org/journals/bull/2009-46-01/S0273-0979-08-01228-7/… – Willie Wong Mar 6 '12 at 7:58