3 problems

Second Hamiltonian structure conjecture. The equation possesses a second Hamiltonian structure, whose form is more complicated than the one displayed above. The conjecture asserts…

Let ${\cal Q}_n^{(Q)}$ and ${\cal P}_n^{(Q)}$ denote the corresponding higher Poisson structures in the $Q$-space, and consider the part of ${\cal P}_n^{(Q)}$ represented by the di…

Commutativity conjecture. The Hamiltonian PDEs $\frac{du}{dt_n}=P_n$, $n\in\mathbb{Z}_+$, form a compatible hierarchy; equivalently, $[P_m,P_n]=0$ for every $m,n\in\mathbb{Z}_+$. A…