Numerical study of blow-up mechanisms for Davey-Stewartson II systems
Analysis of PDEs
2017-12-27 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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 critical nonlinear Schr\"odinger equations. The blow-up profile is given by a dynamically rescaled lump.
Keywords
Cite
@article{arxiv.1712.08814,
title = {Numerical study of blow-up mechanisms for Davey-Stewartson II systems},
author = {C. Klein and N. Stoilov},
journal= {arXiv preprint arXiv:1712.08814},
year = {2017}
}