# Anomalous correlators, "ghost" waves and nonlinear standing waves in the $\beta$-FPUT system

@article{Zaleski2019AnomalousC, title={Anomalous correlators, "ghost" waves and nonlinear standing waves in the \$\beta\$-FPUT system}, author={Joseph Zaleski and Miguel Onorato and Yuri V. Lvov}, journal={arXiv: Chaotic Dynamics}, year={2019} }

We show that Hamiltonian nonlinear dispersive wave systems with cubic nonlinearity and random initial data develop, during their evolution, anomalous correlators. These are responsible for the appearance of "ghost" excitations, i.e. those characterized by negative frequencies, in addition to the positive ones predicted by the linear dispersion relation. We use generalization of the Wick's decomposition and the wave turbulence theory to explain theoretically the existence of anomalous…

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