Applied Math Seminar Announcement

A new formalism for description of modulation processes is proposed. The method is applied to the difficult problem of multi-phase modulations of deep water waves. The approach results in a system of PDEs that describe the dynamics of the spectra near each peak of the spectrum. As a result, the method may be regarded as an extension of two existing approaches: of the discrete modes description for a few modes, or slow modulation of one mode (resulting in equation of Ginzburg-Landau type). The equations given by the method may be considered as an alternative to the well-known integral Zakharov equation in the context of deep water waves problem. Potentially, the formalism will find an application in a very broad range of physical situations with multi-phase dynamics.