Envelope solitons with stationary crests

Publisher Website
Google Scholar
Abstract
Recent analytical and numerical work has shown that gravity–capillary surface waves as well as other dispersive wave systems support symmetric solitary waves with decaying oscillatory tails, which bifurcate from linear periodic waves at an extremum value of the phase speed. It is pointed out here that, for small amplitudes, these solitary waves can be interpreted as particular envelope‐soliton solutions of the nonlinear Schrödinger equation, such that the wave crests are stationary in the reference frame of the wave envelope. Accordingly, these waves (and their three‐dimensional extensions) are expected to be unstable to oblique perturbations.