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Article Dans Une Revue Studies in Applied Mathematics Année : 2018

Numerical Study of Blow-Up Mechanisms for Davey-Stewartson II Systems

Résumé

We present a detailed numerical study of various blow‐up issues in the context of the focusing Davey–Stewartson II equation. To this end, we study Gaussian initial data and perturbations of the lump and the explicit blow‐up solution due to Ozawa. Based on the numerical results it is conjectured that the blow‐up in all cases is self‐similar, and that the time‐dependent scaling behaves as in the Ozawa solution and not as in the stable blow‐up of standard $L^2$ critical nonlinear Schrödinger equation. The blow‐up profile is given by a dynamically rescaled lump.

Dates et versions

hal-01899977 , version 1 (20-10-2018)

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Christian Klein, Nikola M. Stoilov. Numerical Study of Blow-Up Mechanisms for Davey-Stewartson II Systems. Studies in Applied Mathematics, 2018, 141 (1), pp.89-112. ⟨10.1111/sapm.12214⟩. ⟨hal-01899977⟩
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