In textbooks on classical mechanics, the exactly solvable models are all separable. Is there any model integrable but not separable?
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1$\begingroup$ Related to Is a system integrable if and only if its Hamilton-Jacobi equation is separable? $\endgroup$– DiracologyFeb 2, 2018 at 12:52
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/291511/2451 and links therein. $\endgroup$– Qmechanic ♦Feb 2, 2018 at 13:40
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The Toda-Lattice is integrable but not seperable https://en.wikipedia.org/wiki/Toda_lattice#Integrability
Im still learning all of this so I‘am unable to tell you why, but that‘s the example my professor gave.