CAPILLARY-GRAVITY PERIODIC AND SOLITARY WAVES

It is now well-known that capillary-gravity waves of solitary type exist in deep water. These waves bifurcate from a train of trivial periodic waves when the wave number corresponds to the minimum of the dispersion curve. Such solitary waves are characterized by decaying oscillations in their tail. In this Letter, it is shown how these recently discovered waves can be obtained as the limit of periodic waves as the wavelength is continuously increased. Moreover, the existence of new branches of solitary waves is conjectured.