EXISTENCE OF A GENERALIZED SOLITARY WAVE SOLUTION FOR WATER WITH POSITIVE BOND NUMBER LESS THAN 1/3

The objective of this paper is to give a rigorous answer to the question whether there exists a generalized solitary wave of elevation on water when the nondimensional surface tension coefficient, the so-called Bond number, is positive but less than 1 3 and the Froude number is near 1 but greater than 1. The main difficulties to overcome are the small amplitude oscillations at infinity and the choice of appropriate Banach spaces for the solution of the problem. It is shown that an asymptotic expansion developed for this problem indeed yields an approximate solitary wave solution to the exact equations. © 1991.