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

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 infinity under NV dynamics for large $t$. This reflects the paper's numerical observation that NV behaves qualitatively like the KPII equation for large negative $E$; no analytical resolution is given.