Spectral filtering formalism and its application for multi-phase deep-water wavetrains

A new formalism of spectral filtering for the description of the modulation processes is proposed. The method allows one to study the classical problem of multi-phase modulations in dispersive systems. In the present paper, deep-water waves are considered. Spectral filtering results in a system of coupled equations that describe the modulations of the carrier wave and its harmonics. The formalism may find applications in a broad range of physical situations with multi-phase dynamics