Some properties of deep water solitons

Abstract

Envelope solitons for surface waves in deep water are studied using the coupled equation for the Fourier amplitudes of the surface displacement. Comparison is made with some wave-tank experiments of Feir. A linear stability analysis is made for an imposed transverse ripple. A slowly growing instability is found at wavelengths comparable to, or longer than, the length of the soliton. A slowly developing instability is also found for a soliton propagating through a train of waves of wavelength appreciably smaller than that of the soliton. A soliton propagating through a train of waves with wavelength much larger than that of the soliton exhibits gross distortion due to the orbital fluid velocity of the wavetrain. This distortion is to some extent reversible, as the soliton tends to ’’recover’’ when the wavetrain is damped to zero amplitude. Some comments are given concerning the statistics of a wave field containing solitons.