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Pré-Publication, Document De Travail Année : 2021

Large Deviations Principle for the Cubic NLS Equation

Résumé

In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrödinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue waves in deep sea. Our results are twofold: first, we introduce a notion of criticality and prove a Large Deviations Principle (LDP) for the subcritical and critical cases. Second, we study the most likely initial conditions that lead to the formation of a rogue wave, from a theoretical and numerical point of view. Finally, we propose several open questions for future research.
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Dates et versions

hal-03428570 , version 1 (15-11-2021)

Identifiants

  • HAL Id : hal-03428570 , version 1

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Miguel Angel Garrido, Ricardo Grande, Kristin M Kurianski, Gigliola Staffilani. Large Deviations Principle for the Cubic NLS Equation. 2021. ⟨hal-03428570⟩
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