## 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 L. Swett Mar 5 2012 at 19:05
@TannerL Swett, so oxford definition matches with Wikipedia... Thanks for the commment. – Pradip Mishra Mar 5 2012 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... – Pradip Mishra Mar 5 2012 at 19:22