6533b827fe1ef96bd1286e94
RESEARCH PRODUCT
Numerical Study of Blow-Up Mechanisms for Davey-Stewartson II Systems
Christian KleinNikola Stoilovsubject
Applied MathematicsGaussian010102 general mathematicsMathematics::Analysis of PDEsContext (language use)01 natural sciences010305 fluids & plasmasNonlinear systemsymbols.namesakeMathematics::Algebraic Geometry0103 physical sciencessymbolsApplied mathematics0101 mathematicsNonlinear Sciences::Pattern Formation and SolitonsScalingMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-04-10 | Studies in Applied Mathematics |