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arXiv · 1712.08814

Numerical study of blow-up mechanisms for Davey-Stewartson II systems

C. Klein·N. Stoilov
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Abstract

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 is as in the Ozawa solution and not as in the stable blow-up of standard $L^{2}$ critical nonlinear Schr\"odinger equations. The blow-up profile is given by a dynamically rescaled lump.

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C. Klein, N. Stoilov. 2017-12-23. Numerical study of blow-up mechanisms for Davey-Stewartson II systems. https://arxiv.org/abs/1712.08814

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