8 problems

Let initial data for the Novikov–Veselov equation be classified as critical, subcritical, or supercritical according to the behavior of the associated Schrödinger operator at the z…

Let $E$ satisfy $|E|\ll 10$. A small-energy blow-up conjecture asserts that the KdV soliton for small $a$ is stable under NV dynamics, while the KdV soliton for large $a$ is unstab…

Let $E\ll -1$. A large-negative-energy behavior conjecture asserts that the KdV soliton is stable under NV dynamics and that localized initial data will be radiated away to infinit…

Let $E\gg 1$. A large-positive-energy behavior conjecture asserts that the KdV soliton for small $a$ is stable under NV dynamics, whereas the KdV soliton for large $a$ is unstable…

Rank-condition conjecture. The rank condition for the KP-(II) equation should also hold for $y\gg0$ and $y\ll0$ in the Novikov–Veselov equation. In particular, for the permutation…

Lassas–Mueller–Siltanen conjecture. For $n=3$, the function

Lassas–Mueller–Siltanen conjecture. The function $q(t)$ is a classical solution of the Novikov–Veselov equation

Novikov's conjecture. The inverse problem for the two-dimensional Schrödinger operator at a fixed energy should be completely solvable, and inverse scattering for the Schrödinger e…