Large-positive-energy asymptotic behavior conjecture for the Novikov–Veselov equation

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 under NV dynamics. For large $t$, smaller KdV solitons, lumps, and radiation will appear, and localized initial data will develop into radiation and lumps. This is a numerical conjecture about the qualitative long-time behavior of NV, which behaves like the KPI equation for large positive $E$; its claims are based on observed stability, instability, and lump formation rather than an analytical proof.