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Feb 15, 2010 at 17:57 comment added José Figueroa-O'Farrill My guess -- I'll try to confirm -- is that this is probably the trace of the square of the Lax operator for this model.
Feb 15, 2010 at 17:09 comment added Greg Muller Do you happen to know where the third integral of motion comes from? For my purposes, I don't really need a complete set of $n$ integrals of motion, I really only need the natural analog of the third integral of motion, after momentum and energy. My guess is it has the above form even when there are more particles.
Feb 15, 2010 at 14:27 history answered José Figueroa-O'Farrill CC BY-SA 2.5