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Results tagged with integrable-systems
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user 27069
3
votes
Accepted
Toda Hierarchy and Quantum Cohomology of $\mathbb{P}^1$ Frobenius manifolds
I would say that basically everything you wrote is correct, and in particular the equation $F=\lim_{\epsilon\to 0} \epsilon^2 \log \tau|_{t^{\alpha,p>0}=0,t^{\alpha,0}=t^\alpha}$.
It is true that, mor …
- 654
5
votes
1
answer
825
views
Why is every Hamiltonian system locally integrable?
It is common knowledge that every Hamiltonian system is locally integrable (away from singular points of the Hamiltonian), meaning that, in a neighborhood of each point of the $2n$-dimensional symplec …
- 654
2
votes
Importance of a Hamiltonian integrable system be a bi-Hamiltonian system?
While José's comment pretty much answers this, let me add that, sometimes, it can be hard or impossible to have the system of commuting symmetries $f_j$ under control, and the bihamiltonian recursion …
- 654
6
votes
Accepted
Integrability - conditions of lax pairs
One way to see this, is that you want the zero-curvature representation to be useful and tell you something you didn't know before. Your representation has the problem of being singular, in the sense …
- 654