WATER-WAVES FOR SMALL SURFACE-TENSION - AN APPROACH VIA NORMAL-FORM

In this paper we determine the possible crest-forms of permanent waves of small amplitude which exist on the free surface of a two-dimensional fluid layer under the influence of gravity and surface tension when the Froude number lambda is close to 1. The Bond number b, measuring surface tension, is assumed to satisfy b < 1/3. We find one-parameter families of periodic waves of two different types, quasiperiodic waves and solitary waves with oscillations at infinity. The existence of true solitary waves is established for a sequence of systems approximating the full Euler equations in every algebraic order of lambda - 1.