A note on the application of Whitham's method to nonlinear waves in dispersive media

In this paper, a method developed by Whitham for obtaining equations governing the slow variation of finite-amplitude wave trains, is slightly modified. The relevant equations describing wave-wave interaction, and self-action are derived. The stability of a finite-amplitude wave train is treated in two different ways. The possibility of having a ‘solitary modulation’ on a finite-amplitude wave train is pointed out.