Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation Article - Juillet 2017

Anna Kazeykina, Christian Klein

Anna Kazeykina, Christian Klein, « Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation  », Nonlinearity, juillet 2017, pp. 2566 - 2591. ISSN 0951-7715

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| -> infinity, 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.

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