ON THE USE OF TRICOHERENT ANALYSIS TO DETECT NONLINEAR WAVE-WAVE INTERACTIONS

For the description of non-linear effects in dispersive media, the app roach of three- and four-wave interactions may be used. Higher-order s pectral analysis is required for identifying interacting waves in rand om signals. The bicoherence spectrum, which is the normalized cumulant spectrum of the third order, has been applied to numerous studies for analysing three-wave interactions in numerical, laboratory and natura l experiments. Here, we develop the tricoherence spectrum to detect fo ur-wave interactions, calculate statistical properties of the trispect rum and tricoherence estimators as well as the confidence interval for the latter, and present results of numerical estimations of the trico herence using synthetic signals.