  The present study describes, first, an efficient algorithm for computing
capillary-gravity solitary waves solutions of the irrotational Euler equations
with a free surface and, second, provides numerical evidences of the existence
of an infinite number of generalised solitary waves (solitary waves with
undamped oscillatory wings). Using conformal mapping, the unknown fluid domain,
which is to be determined, is mapped into a uniform strip of the complex plane.
In the transformed domain, a Babenko-like equation is then derived and solved
numerically.
