About S-theory verification which is used to describe the wave field modulation instabilities

Abstract

The modulation instability of intense wave field is considered for a model described by the Lighthill equation, taking into account absorption and external source. The nature of the wave appearance and the wave field envelopes of the anomalous amplitude in nonlinear media are discussed, in particular on the ocean surface. The results of the simplified description based on a modified S-theory and the results without the use of simplifications are discussed. Many of the characteristics of both descriptions are close enough for at least in the initial stage of the nonlinear instability mode.