De Sole–Kac–Wakimoto conjecture on normal forms of Hamiltonian operators

Let $H$ be a translation-invariant Hamiltonian operator of order $N\geq 7$. A differential function is quasiconstant if it depends only on $x$.

De Sole–Kac–Wakimoto conjecture. There exists a contact transformation that brings $H$ to either a quasiconstant coefficient skew-adjoint differential operator, or to a linear combination of the operators $H^{(j,0)}$ with $3\leq j\leq N$ and $j$ odd.

This conjecture proposes normal forms for translation-invariant Hamiltonian operators under contact transformations. The paper subsequently formulates stronger conjectures after enlarging the allowed transformations, so this statement is part of a hierarchy of proposed classification results.