Large deviations principle for the cubic NLS equation

被引:3
作者
Garrido, Miguel Angel [1 ]
Grande, Ricardo [2 ]
Kurianski, Kristin M. [3 ]
Staffilani, Gigliola [4 ]
机构
[1] Columbia Univ, Dept Stat, New York, NY USA
[2] Ecole Normale Super, Paris, France
[3] Calif State Univ, Fullerton, CA USA
[4] MIT, Cambridge, MA USA
关键词
NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; HIGH-SOBOLEV-NORMS; ROGUE WAVES; CAUCHY-PROBLEM; GROWTH; SCATTERING; TORI;
D O I
10.1002/cpa.22131
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:4087 / 4136
页数:50
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