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.



What is soliton
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. 


