Timeline for Why is there a connection between enumerative geometry and nonlinear waves?
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| Sep 27 at 22:07 | answer | added | الاسم الاول | timeline score: 1 | |
| Aug 22, 2022 at 11:49 | comment | added | Tom Copeland | For a brief note on hydrodynamics and the KdV equation, see the Wiki article en.wikipedia.org/wiki/…. | |
| Sep 17, 2020 at 17:42 | history | edited | John Baez | CC BY-SA 4.0 |
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| Jun 5, 2015 at 21:48 | comment | added | paul garrett | @DenisSerre... Exactly. This reminds me also of the "mysteries" that are corollaries of the Strong Law of Large Numbers: a particular example satisfies it... because it is universal. | |
| Jun 5, 2015 at 20:45 | comment | added | Denis Serre | Don't think about KdV as a fluid equation. It is just a normal form in the realm of nonlinear dispersive PDEs. You encounter it at every intersection. | |
| May 1, 2015 at 2:05 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Sep 25, 2014 at 0:50 | comment | added | Richard Stanley | Some other references are the five arXiv papers by Yuji Kodama and Lauren Williams. | |
| S Sep 25, 2014 at 0:16 | history | suggested | CommunityBot |
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| Sep 24, 2014 at 23:56 | review | Suggested edits | |||
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| Sep 22, 2014 at 14:56 | answer | added | Tom Copeland | timeline score: 30 | |
| Oct 24, 2013 at 20:13 | comment | added | Nathaniel Bottman | @Javier: thanks! That looks like just what I need. | |
| Oct 24, 2013 at 19:43 | comment | added | Javier Álvarez | Take a look at the relationship between Quantum Cohomology and Integrable Systems as explained in the book by Guest: books.google.es/books?id=SvrSbWoMRdMC&printsec=frontcover | |
| Oct 23, 2013 at 2:16 | comment | added | Peter Samuelson | I think it is certainly an appropriate question, and wish I were able to answer it. | |
| Oct 22, 2013 at 23:17 | comment | added | Tom Copeland | A similar question applies to the inviscid Burgers' equation in relation to the facets of associahedra. See OEIS A086810 and A033282 (On-line Encyclopedia of Integer Sequences). | |
| Oct 22, 2013 at 18:20 | comment | added | Dan Petersen | Moreover, Kontsevich's proof does provide a link to integrable systems -- he rewrites $F$ in terms of a particular matrix integral, and it's known more generally that certain types of matrix integrals give rise to $\tau$-functions of integrable hierarchies. | |
| Oct 22, 2013 at 18:20 | comment | added | Dan Petersen | I'm not an expert, so take this with a grain of salt. I don't think you should search for a direct link between water waves and GW theory. Instead the answer is that water waves are examples of solitons, and that the theory of solitons can be interpreted in terms of integrable systems. Also, there are "moral" reasons for why GW theory should have a link to integrable hierarchies, in this case the KdV hierarchy. | |
| Oct 22, 2013 at 18:08 | history | edited | Qfwfq | CC BY-SA 3.0 |
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| Oct 22, 2013 at 17:15 | history | asked | Nathaniel Bottman | CC BY-SA 3.0 |