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Article Dans Une Revue Nonlinearity Année : 2017

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

Résumé

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.

Dates et versions

hal-01551757 , version 1 (30-06-2017)

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Anna Kazeykina, Christian Klein. Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation. Nonlinearity, 2017, 30 (7), pp.2566 - 2591. ⟨10.1088/1361-6544/aa6f29⟩. ⟨hal-01551757⟩
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