I'm studying some papers about integrable system. And the problem arises in my mind.
When I search papers, there are many papers such as "Kuramoto model in 3-sphere", "Toda Lattice with hyperelliptic Riemann surface", "... system in torus", "... on closed manifolds" etc.
But in the beginning I learned PDE, we never talk about this PDE in what space or in what sense.
If it's possible, please tell me the concept.