Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Origin of heavy tails in equations of the Nonliner Schro ̈dinger type: an exact result M. Onorato, D. Proment, G. El, S. Randoux, P. Suret, The determination of the statistical properties of nonlinear dispersive waves is an important issue in many physical systems. Several research activities have been conducted in order to understand the formation of rogue waves in systems described by envelope equations, such as the Nonliner Schrodinger. Here, we derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonliner Schro ̈dinger equa tion. Numerical simulations are also performed to confirm our findings. Our work sheds some light on the origin of rogue waves in dispersive nonlinear media ruled by local cubic nonlinearity.