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• W2022262454 abstract "The possibility of finite-time, dispersive blow-up for nonlinear equations of Schrödinger type is revisited. This mathematical phenomena is one of the conceivable explanations for oceanic and optical rogue waves. In dimension one, the fact that dispersive blow up does occur for nonlinear Schrödinger equations already appears in [9]. In the present work, the existing results are extended in several ways. In one direction, the theory is broadened to include the Davey–Stewartson and Gross–Pitaevskii equations. In another, dispersive blow up is shown to obtain for nonlinear Schrödinger equations in spatial dimensions larger than one and for more general power-law nonlinearities. As a by-product of our analysis, a sharp global smoothing estimate for the integral term appearing in Duhamel's formula is obtained. On revisite la possibilité de la formation de singularités dispersives (dispersive blow-up) pour des solutions d'équations de Schrödinger non linéaires. Ce phénomène mathématique pourrait être une explication pour l'apparition des “vagues scélérates” (rogue waves) en océanographie et optique non linéaire. L'émergence de singularités dispersives pour des équations de Schrödinger non linéaires en dimension spatiale un a été montrée dans [9]. Ces résultats sont étendus ici dans plusieurs directions. D'une part, la théorie est étendue à des équations de Schrödinger en dimension spatiale quelconque, avec des non-linéarités de type puissance générales. D'autre part, on traite également le cas des systèmes de Davey–Stewartson et de l'équation de Gross–Pitaevskii. Un sous-produit de l'analyse est un effet de lissage global précis pour le terme intégral de la représentation de Duhamel." @default.
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• W2022262454 date "2014-10-01" @default.
• W2022262454 modified "2023-10-18" @default.
• W2022262454 title "Dispersive blow-up for nonlinear Schrödinger equations revisited" @default.
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• W2022262454 doi "https://doi.org/10.1016/j.matpur.2014.02.006" @default.
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