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arXiv · 1607.01987

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

A. Kazeykina·C. Klein
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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.

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BibTeXRIS

A. Kazeykina, C. Klein. 2016-07-07. Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation. https://doi.org/10.1088/1361-6544/aa6f29

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