In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrodinger 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.

Large deviations principle for the cubic NLS equation / Garrido, M. A.; Grande Izquierdo, R.; Kurianski, K. M.; Staffilani, G.. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - 76:12(2023), pp. 4087-4136. [10.1002/cpa.22131]

Large deviations principle for the cubic NLS equation

Grande Izquierdo, R.
;
Staffilani, G.
2023-01-01

Abstract

In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schrodinger 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.
2023
76
12
4087
4136
https://doi.org/10.1002/cpa.22131
https://arxiv.org/abs/2110.15748
Garrido, M. A.; Grande Izquierdo, R.; Kurianski, K. M.; Staffilani, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135360
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