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I am wondering if anyone has ever come up with a mathematical description of something that (to me, and I am no expert) look like soliton vortexes.

The example I can think of is if you create two vortexes, one spinning clockwise, and the other anticlockwise, on the surface of water. In the following video, this is done using a ceramic plate: http://www.youtube.com/watch?v=pnbJEg9r1o8. You immerse the plate in the water, perpendicular to the surface of the water, and move the plate in a direction perpendicular to its surface, and finally extract the plate.

Can questions such as: is this a soliton? Does it exist? What is the time of existence? etc... be answered from the Euler / Navier Stokes Equations? Quick look on the arXiv made me a little confused.

Any help or reference will be appreciated.

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    $\begingroup$ I'm not sure what you mean by "mathematical descriptions". Soliton solutions are often given in mathematical terms, can you be more precise what you are searching for? $\endgroup$
    – ACuriousMind ♦
    Commented Feb 18, 2016 at 1:03
  • $\begingroup$ @ACuriousMind I'd like to see exactly that: an explicit (or otherwise constructed) solution to Euler or Navier-Stokes (possibly an associated free boundary problem taking care of the surface of the water) which possesses these properties: it looks like one of those two-ended vortices and disperses in finite time. $\endgroup$
    – snefs
    Commented Feb 18, 2016 at 3:15

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