Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation

Abstract

We study numerically the evolution of perturbed Korteweg-de Vries solitons and of well localized initial data by the Novikov-Veselov (NV) equation at different levels of the "energy" parameter $E$. We show that as $|E| \to \infty$, NV behaves, as expected, similarly to its formal limit, the Kadomtsev-Petviashvili equation. However at intermediate regimes, i.e. when $| E |$ is not very large, more varied scenarios are possible, in particular, blow-ups are observed. The mechanism of the blow-up is studied