The Top 10 Differential Equations of All Time

Now that I know that I am providing endless amusement to the grad students, faculty, and (dare-I-say) postdocs in OCIAM, here's a little survey that I have been meaning to do for a while.

Basically, I want to write (or co-write, if anybody else is interested) an article for a venue like the AMS Notices or American Mathematical Monthly that discusses the "top 10 differential equations of all time" (a la David Letterman). The thing is that I need some sort of survey first, so if I just choose 10 that I like, it would be geared too much towards specific subjects. So, if anybody wants to pipe in here, by e-mail, or by any other venue, I would be greatly appreciative. (List of differential equations written on napkins are particularly encouraged, but toilet paper is right out.)

I'd like to get enough lists from people so that I can take the 10 most popular choices from that list and write the article. For each equation, I'd include some (reasonably brief) discussion of where it comes from and why it's important.

Here is a list that partially reflects my opinion but also reflects how little time I'm going to spend typing up the rest of this entry:

10. Lorentz equations

9. the Nesterenko equation*

8. the Klausmeier equation (because it's named after a former colleague who made a great Thanksgiving turkey)

7. Duffing's equation

6. Einstein's field equations (if for no other reason than because it made a guest appearance in The Triplets of Bellevile, and I got a free book out of that)

5. Navier-Stokes equations

4. the linear Schrodinger equation

3. the complex Ginzburg-Landau equation

2. the cubic nonlinear Schrodinger equation (aka, the Gross-Pitaevskii equation) [notice the correlations from 2-4; that's why I need help writing this list]

1. x' = 0


Honorable mention: That equation I "derived" on my AMa 95b final back in the day. (Actually, I could have mentioned any number of courses here, and I think 95b is one of the few in which I didn't develop my own equation of one sort or another with some misplaced derivation. But it amuses me to attribute this to AMa 95, so I won't let the truth get in the way of a good story.)

* This is the "unnamed" equation in a recent paper of mine (and several upcoming ones!) that my collaborators and I decided to name after the person who first derived it because it makes citing his results less cumbersome for the exposition. I wonder if this is how other equations have gotten named?

I swear I'm going to write my review for Avenue Q in the relatively near future.