Scrolling innocently through a paper, when suddenly:pic.twitter.com/LDQTRYH978
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I don't know what that means -- I mean integrable in the sense of "integrable systems," i.e. given arbitrary initial conditions there is a unique holomorphic solution.
ah, i see.. sometimes in physics the term is used to mean you can write the general solution in integral form
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Ah, gotcha! That actually is true in this case, I think, at least in principle. That said, the solutions are related to Painleve transcendents and (as you might expect from the name) can't in general be written in terms of only elementary functions...
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'Integrable' is one of those terms (like 'normal') that has way too many meanings. Luckily, several of them are related to each other! Liouville integrability of a Hamiltonian system is Frobenius integrability of the constants' level sets (or dually, their Ham. vec. fields)
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